# zbMATH — the first resource for mathematics

Compute Distance To:
 Author ID: constantin.adrian Published as: Constantin, A.; Constantin, Adrian Homepage: https://ufind.univie.ac.at/de/person.html?id=36146 External Links: MGP · Wikidata · ORCID · ResearchGate · dblp · GND
 Documents Indexed: 190 Publications since 1990, including 5 Books
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#### Co-Authors

 105 single-authored 21 Escher, Joachim 13 Strauss, Walter Alexander 11 Ivanov, Rossen I. 10 Kolev, Boris 8 Johnson, Robin Stanley 4 Lenells, Jonatan 4 Villari, Gabriele 3 Bressan, Alberto 3 Krishnamurthy, Vikas S. 3 Molinet, Luc 2 Aleman, Alexandru 2 Crowdy, Darren Gregory 2 Ehrnström, Mats 2 Gerdzhikov, Vladimir Stefanov 2 Kalimeris, Konstantinos 2 Scherzer, Otmar 2 Vărvărucă, Eugen 2 Wheeler, Miles H. 1 Clamond, Didier 1 Germain, Pierre 1 Hsu, Hung-Chu 1 Kappeler, Thomas 1 Lannes, David 1 Martin, Calin-Iulian 1 McKean, Henry P. jun. 1 Monismith, Stephen G. 1 Peszat, Szymon 1 Prodanov, Emil M. 1 Topalov, Peter J. 1 Wahlén, Erik 1 Wunsch, Marcus 1 Yin, Zhaoyang
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#### Serials

 9 Archive for Rational Mechanics and Analysis 8 Journal of Fluid Mechanics 6 Communications on Pure and Applied Mathematics 6 Journal of Mathematical Analysis and Applications 6 Journal of Nonlinear Mathematical Physics 4 Physics Letters. A 4 Analele Universităţii din Timişoara. Ştiinţe Matematice 4 Journal of Differential Equations 4 Discrete and Continuous Dynamical Systems 4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Comptes Rendus Mathématiques de l’Académie des Sciences 3 Stochastic Analysis and Applications 3 Differential and Integral Equations 3 Journal of Physics A: Mathematical and General 3 Expositiones Mathematicae 3 Journal of Nonlinear Science 3 Journal of Mathematical Fluid Mechanics 2 Communications in Mathematical Physics 2 Inverse Problems 2 Wave Motion 2 Fluid Dynamics Research 2 Acta Mathematica 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Annali dell’Università di Ferrara. Nuova Serie. Sezione VII 2 Indian Journal of Mathematics 2 Mathematische Annalen 2 Mathematica Japonica 2 Proceedings of the Japan Academy. Series A 2 Publicationes Mathematicae 2 Zbornik Radova. Prirodno-Matematichkog Fakulteta. Serija za Matematiku 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Bollettino della Unione Matemàtica Italiana. Serie VII. A 2 NoDEA. Nonlinear Differential Equations and Applications 2 Nonlinear Analysis. Real World Applications 2 Communications on Pure and Applied Analysis 2 Oberwolfach Reports 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Nonlinearity 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Annales de l’Institut Fourier 1 Archiv der Mathematik 1 Bulletin of the Calcutta Mathematical Society 1 Commentarii Mathematici Helvetici 1 Demonstratio Mathematica 1 Duke Mathematical Journal 1 Ganita 1 Glasgow Mathematical Journal 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of Functional Analysis 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Portugaliae Mathematica 1 Quarterly of Applied Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Studies in Applied Mathematics 1 Rendiconti del Seminario Matematico 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Note di Matematica 1 Rendiconti. Scienze Matemàtiche e Applicazioni. A 1 Annals of Global Analysis and Geometry 1 Physica D 1 Applied Mathematics Letters 1 Publicacions Matemàtiques 1 European Journal of Applied Mathematics 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Communications in Partial Differential Equations 1 L’Enseignement Mathématique. 2e Série 1 Rendiconti del Seminario della Facoltà di Scienze dell’ Università di Cagliari 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Stochastics and Stochastics Reports 1 Publikacije Elektrotehničkog Fakulteta. Serija: Matematika 1 Physics of Fluids 1 Nonlinear World 1 Annales Mathématiques Blaise Pascal 1 Bulletin des Sciences Mathématiques 1 Journal of Applied Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 European Journal of Mechanics. B. Fluids 1 Annals of Mathematics. Second Series 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Analysis and Applications (Singapore) 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Lecture Notes in Mathematics 1 London Mathematical Society Student Texts 1 Journal of Physics A: Mathematical and Theoretical 1 Nonlinear Analysis. Theory, Methods & Applications ...and 2 more Serials
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#### Fields

 109 Partial differential equations (35-XX) 87 Fluid mechanics (76-XX) 35 Ordinary differential equations (34-XX) 26 Dynamical systems and ergodic theory (37-XX) 20 Geophysics (86-XX) 11 Probability theory and stochastic processes (60-XX) 10 Operator theory (47-XX) 8 Integral equations (45-XX) 8 General topology (54-XX) 8 Global analysis, analysis on manifolds (58-XX) 6 General and overarching topics; collections (00-XX) 3 Mechanics of particles and systems (70-XX) 3 Mechanics of deformable solids (74-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

154 Publications have been cited 9,634 times in 1,955 Documents Cited by Year
Wave breaking for nonlinear nonlocal shallow water equations. Zbl 0923.76025
1998
The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations. Zbl 1169.76010
2009
Stability of peakons. Zbl 1049.35149
2000
Global conservative solutions of the Camassa-Holm equation. Zbl 1105.76013
2007
The trajectories of particles in Stokes waves. Zbl 1108.76013
2006
Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation. Zbl 0934.35153
1998
On the scattering problem for the Camassa-Holm equation. Zbl 0999.35065
2001
A shallow water equation on the circle. Zbl 0940.35177
Constantin, A.; McKean, H. P.
1999
Global existence and blow-up for a shallow water equation. Zbl 0918.35005
1998
Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Zbl 0944.35062
2000
Global dissipative solutions of the Camassa-Holm equation. Zbl 1139.35378
2007
Analyticity of periodic traveling free surface water waves with vorticity. Zbl 1228.35076
2011
Global weak solutions for a shallow water equation. Zbl 1002.35101
2000
Particle trajectories in solitary water waves. Zbl 1126.76012
2007
On an integrable two-component Camassa-Holm shallow water system. Zbl 1227.76016
2008
Nonlinear water waves with applications to wave-current interactions and tsunamis. Zbl 1266.76002
2011
Geodesic flow on the diffeomorphism group of the circle. Zbl 1037.37032
2003
Exact steady periodic water waves with vorticity. Zbl 1038.76011
2004
Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044
2006
Stability of the Camassa-Holm solitons. Zbl 1022.35053
Constantin, A.; Strauss, W. A.
2002
On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Zbl 0954.35136
2000
On the inverse spectral problem for the Camassa-Holm equation. Zbl 0907.35009
1998
Pressure beneath a Stokes wave. Zbl 1423.76061
2010
Stability of a class of solitary waves in compressible elastic rods. Zbl 1115.74339
2000
On the deep water wave motion. Zbl 0982.76015
2001
On the Cauchy problem for the periodic Camassa-Holm equation. Zbl 0889.35022
1997
On geodesic exponential maps of the Virasoro group. Zbl 1121.35111
Constantin, A.; Kappeler, T.; Kolev, B.; Topalov, P.
2007
Global weak solutions for a shallow water equation. Zbl 0930.35133
1998
On the geometric approach to the motion of inertial mechanical systems. Zbl 1039.37068
2002
Edge waves along a sloping beach. Zbl 1005.76009
2001
Symmetry of steady periodic surface water waves with vorticity. Zbl 1050.76007
2004
Symmetry of steady periodic gravity water waves with vorticity. Zbl 1151.35076
Constantin, Adrian; Ehrnström, Mats; Wahlén, Erik
2007
Finite propagation speed for the Camassa-Holm equation. Zbl 1076.35109
2005
Steady periodic water waves with constant vorticity: Regularity and local bifurcation. Zbl 1229.35203
2011
Global solutions of the Hunter–Saxton equation. Zbl 1108.35024
2005
Inverse scattering transform for the Degasperis-Procesi equation. Zbl 1211.37081
Constantin, Adrian; Ivanov, Rossen I.; Lenells, Jonatan
2010
Orbital stability of solitary waves for a shallow water equation. Zbl 0984.35139
2001
Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis. Zbl 1135.76007
Constantin, A.; Johnson, R. S.
2008
On the blow-up of solutions of a periodic shallow water equation. Zbl 0960.35083
Constantin, A.
2000
Global bifurcation of steady gravity water waves with critical layers. Zbl 1375.35294
Constantin, Adrian; Strauss, Walter; Vărvărucă, Eugen
2016
Particle trajectories in extreme Stokes waves. Zbl 1250.35150
2012
Periodic traveling gravity water waves with discontinuous vorticity. Zbl 1269.76024
2011
Symmetry of steady deep-water waves with vorticity. Zbl 1125.76007
2004
Stability properties of steady water waves with vorticity. Zbl 1125.35081
2007
Particle trajectories in linear water waves. Zbl 1162.76316
2008
Gerstner waves in the presence of mean currents and rotation. Zbl 1387.86009
Constantin, A.; Monismith, S. G.
2017
The Hamiltonian structure of the Camassa-Holm equation. Zbl 0881.35094
1997
Recovery of steady periodic wave profiles from pressure measurements at the bed. Zbl 1284.76065
Clamond, D.; Constantin, A.
2013
On the existence of positive solutions of second order differential equations. Zbl 1223.34041
2005
Particle trajectories in linear deep-water waves. Zbl 1154.35429
Constantin, Adrian; Ehrnström, Mats; Villari, Gabriele
2008
Rotational steady water waves near stagnation. Zbl 1152.76328
2007
Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates. Zbl 1404.86015
Constantin, A.; Johnson, R. S.
2017
Harmonic maps and ideal fluid flows. Zbl 1290.76014
Aleman, A.; Constantin, A.
2012
On the structure of a family of quasilinear equations arising in shallow water theory. Zbl 0923.76028
1998
The theorem of Kerékjártó on periodic homeomorphisms of the disc and the sphere. Zbl 0852.57012
1994
Hamiltonian formulation for wave-current interactions in stratified rotational flows. Zbl 1344.35084
Constantin, A.; Ivanov, R. I.; Martin, C.-I.
2016
Pressure beneath a solitary water wave: mathematical theory and experiments. Zbl 1281.76024
Constantin, Adrian; Escher, Joachim; Hsu, Hung-Chu
2011
Exact periodic traveling water waves with vorticity. Zbl 1020.35012
2002
A Hamiltonian approach to wave-current interactions in two-layer fluids. Zbl 1326.76021
Constantin, A.; Ivanov, R. I.
2015
Integrability of invariant metrics on the diffeomorphism group of the circle. Zbl 1170.37336
Constantin, A.; Kolev, B.
2006
The initial value problem for a generalized Boussinesq equation. Zbl 1161.35445
2002
Global solutions for quasilinear parabolic problems. Zbl 1004.35070
2002
Positive solutions of quasilinear elliptic equations. Zbl 0891.35033
1997
On the recovery of solitary wave profiles from pressure measurements. Zbl 1248.76025
Constantin, A.
2012
Mean velocities in a Stokes wave. Zbl 1320.76016
2013
Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train. Zbl 1222.76020
Constantin, A.
2011
Nearly-Hamiltonian structure for water waves with constant vorticity. Zbl 1162.76315
Constantin, Adrian; Ivanov, Rossen I.; Prodanov, Emil M.
2008
On equatorial wind waves. Zbl 1289.86002
2013
Equatorial wave-current interactions. Zbl 1421.35102
Constantin, A.; Ivanov, R. I.
2019
Positive solutions of Schrödinger equations in two-dimensional exterior domains. Zbl 0866.35031
1997
Existence of positive solutions of quasilinear elliptic equations. Zbl 0878.35040
1996
Dressing method for the Degasperis-Procesi equation. Zbl 1365.35134
2017
On the non-dimensionalisation, scaling and resulting interpretation of the classical governing equations for water waves. Zbl 1362.35257
2008
On the inverse scattering approach to the Camassa-Holm equation. Zbl 1038.35067
2003
Positive solutions of quasilinear elliptic equations in two-dimensional exterior domains. Zbl 0974.35033
2000
On the spectral problem for the periodic Camassa-Holm equation. Zbl 0881.35102
1997
Global solutions of perturbed differential equations. Zbl 0839.34002
1995
Global solutions for quasilinear parabolic systems. Zbl 1043.35066
Constantin, Adrian; Escher, Joachim; Yin, Zhaoyang
2004
A penalization method for calculating the flow beneath traveling water waves of large amplitude. Zbl 1321.35146
Constantin, A.; Kalimeris, K.; Scherzer, O.
2015
A general-weight Sturm-Liouville problem. Zbl 0913.34022
1997
Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045
2007
Approximations of steady periodic water waves in flows with constant vorticity. Zbl 1330.76020
Constantin, A.; Kalimeris, K.; Scherzer, O.
2015
Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity. Zbl 1282.35283
2012
On the inviscid Proudman-Johnson equation. Zbl 1179.35236
2009
On an infinite interval boundary value problem. Zbl 0969.34024
1999
Quasi-periodicity with respect to time of spatially periodic finite-gap solutions of the Camassa-Holm equation. Zbl 0923.35126
1998
On the Cauchy problem for a family of quasilinear hyperbolic equations. Zbl 0913.35091
1998
The flow beneath a periodic travelling surface water wave. Zbl 1310.76019
2015
On Nagumo’s theorem. Zbl 1192.34014
2010
On the particle paths in solitary water waves. Zbl 1185.35182
2010
Global existence for fully parabolic boundary value problems. Zbl 1108.35091
2006
A dynamical systems approach towards isolated vorticity regions for tsunami background states. Zbl 1294.35169
2011
On the relevance of soliton theory to tsunami modelling. Zbl 1231.76027
2009
Integrability of invariant metrics on the Virasoro group. Zbl 1195.58006
Constantin, A.; Kolev, B.; Lenells, J.
2006
Poisson structure and action-angle variables for the Camassa-Holm equation. Zbl 1137.37032
2006
On the inverse scattering approach for an integrable shallow water wave equation. Zbl 1010.76011
2003
Soliton interactions for the Camassa-Holm equation. Zbl 0879.35121
1997
On the asymptotic behavior of second order nonlinear differential equations. Zbl 0808.34050
Constantin, A.
1993
The time evolution of the maximal horizontal surface fluid velocity for an irrotational wave approaching breaking. Zbl 1337.76008
Constantin, A.
2015
On the oscillation of solutions of the Liénard equation. Zbl 0877.34028
1997
Equatorial wave-current interactions. Zbl 1421.35102
Constantin, A.; Ivanov, R. I.
2019
Stuart-type vortices on a rotating sphere. Zbl 1429.76038
2019
Steady point vortex pair in a field of Stuart-type vorticity. Zbl 1419.76105
Krishnamurthy, Vikas S.; Wheeler, Miles H.; Crowdy, Darren G.; Constantin, Adrian
2019
Gerstner waves in the presence of mean currents and rotation. Zbl 1387.86009
Constantin, A.; Monismith, S. G.
2017
Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates. Zbl 1404.86015
Constantin, A.; Johnson, R. S.
2017
Dressing method for the Degasperis-Procesi equation. Zbl 1365.35134
2017
Global bifurcation of steady gravity water waves with critical layers. Zbl 1375.35294
Constantin, Adrian; Strauss, Walter; Vărvărucă, Eugen
2016
Hamiltonian formulation for wave-current interactions in stratified rotational flows. Zbl 1344.35084
Constantin, A.; Ivanov, R. I.; Martin, C.-I.
2016
Exact travelling periodic water waves in two-dimensional irrotational flows. Zbl 1354.76024
2016
Preface. Zbl 1354.00089
Constantin, A. (ed.); Escher, J. (ed.); Johnson, R. S. (ed.); Villari, G. (ed.)
2016
Fourier analysis. Part I: Theory. Zbl 1359.42001
2016
Nonlinear water waves. Cetraro, Italy, June 24–28, 2013. Zbl 1348.76002
2016
A Hamiltonian approach to wave-current interactions in two-layer fluids. Zbl 1326.76021
Constantin, A.; Ivanov, R. I.
2015
A penalization method for calculating the flow beneath traveling water waves of large amplitude. Zbl 1321.35146
Constantin, A.; Kalimeris, K.; Scherzer, O.
2015
Approximations of steady periodic water waves in flows with constant vorticity. Zbl 1330.76020
Constantin, A.; Kalimeris, K.; Scherzer, O.
2015
The flow beneath a periodic travelling surface water wave. Zbl 1310.76019
2015
The time evolution of the maximal horizontal surface fluid velocity for an irrotational wave approaching breaking. Zbl 1337.76008
Constantin, A.
2015
Stokes waves in water with a non-flat bed. Zbl 1446.76078
Constantin, A.
2014
Recovery of steady periodic wave profiles from pressure measurements at the bed. Zbl 1284.76065
Clamond, D.; Constantin, A.
2013
Mean velocities in a Stokes wave. Zbl 1320.76016
2013
On equatorial wind waves. Zbl 1289.86002
2013
Particle trajectories in extreme Stokes waves. Zbl 1250.35150
2012
Harmonic maps and ideal fluid flows. Zbl 1290.76014
Aleman, A.; Constantin, A.
2012
On the recovery of solitary wave profiles from pressure measurements. Zbl 1248.76025
Constantin, A.
2012
Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity. Zbl 1282.35283
2012
Introduction: Nonlinear water waves. Zbl 1250.76018
2012
On the open sea propagation of water waves generated by a moving bed. Zbl 1250.86005
2012
On the geometry of the diffeomorphism group of the circle. Zbl 1257.58005
2012
Analyticity of periodic traveling free surface water waves with vorticity. Zbl 1228.35076
2011
Nonlinear water waves with applications to wave-current interactions and tsunamis. Zbl 1266.76002
2011
Steady periodic water waves with constant vorticity: Regularity and local bifurcation. Zbl 1229.35203
2011
Periodic traveling gravity water waves with discontinuous vorticity. Zbl 1269.76024
2011
Pressure beneath a solitary water wave: mathematical theory and experiments. Zbl 1281.76024
Constantin, Adrian; Escher, Joachim; Hsu, Hung-Chu
2011
Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train. Zbl 1222.76020
Constantin, A.
2011
A dynamical systems approach towards isolated vorticity regions for tsunami background states. Zbl 1294.35169
2011
Pressure beneath a Stokes wave. Zbl 1423.76061
2010
Inverse scattering transform for the Degasperis-Procesi equation. Zbl 1211.37081
Constantin, Adrian; Ivanov, Rossen I.; Lenells, Jonatan
2010
On Nagumo’s theorem. Zbl 1192.34014
2010
On the particle paths in solitary water waves. Zbl 1185.35182
2010
Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis. Zbl 1350.76008
2010
Trochoidal solutions to the incompressible two-dimensional Euler equations. Zbl 1195.76134
2010
The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations. Zbl 1169.76010
2009
On the inviscid Proudman-Johnson equation. Zbl 1179.35236
2009
On the relevance of soliton theory to tsunami modelling. Zbl 1231.76027
2009
On the propagation of tsunami waves, with emphasis on the tsunami of 2004. Zbl 1180.35441
2009
On an integrable two-component Camassa-Holm shallow water system. Zbl 1227.76016
2008
Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis. Zbl 1135.76007
Constantin, A.; Johnson, R. S.
2008
Particle trajectories in linear water waves. Zbl 1162.76316
2008
Particle trajectories in linear deep-water waves. Zbl 1154.35429
Constantin, Adrian; Ehrnström, Mats; Villari, Gabriele
2008
Nearly-Hamiltonian structure for water waves with constant vorticity. Zbl 1162.76315
Constantin, Adrian; Ivanov, Rossen I.; Prodanov, Emil M.
2008
On the non-dimensionalisation, scaling and resulting interpretation of the classical governing equations for water waves. Zbl 1362.35257
2008
Global conservative solutions of the Camassa-Holm equation. Zbl 1105.76013
2007
Global dissipative solutions of the Camassa-Holm equation. Zbl 1139.35378
2007
Particle trajectories in solitary water waves. Zbl 1126.76012
2007
On geodesic exponential maps of the Virasoro group. Zbl 1121.35111
Constantin, A.; Kappeler, T.; Kolev, B.; Topalov, P.
2007
Symmetry of steady periodic gravity water waves with vorticity. Zbl 1151.35076
Constantin, Adrian; Ehrnström, Mats; Wahlén, Erik
2007
Stability properties of steady water waves with vorticity. Zbl 1125.35081
2007
Rotational steady water waves near stagnation. Zbl 1152.76328
2007
Generalized Fourier transform for the Camassa-Holm hierarchy. Zbl 1127.35045
2007
Introduction: Some recent developments of nonlinear water wave theory. Zbl 1152.76327
2007
Solitons from the Lagrangian perspective. Zbl 1135.35066
2007
The Camassa-Holm equation as a geodesic flow for the $$H^1$$ right-invariant metric. Zbl 1144.53328
Constantin, A.; Ivanov, R. I.
2007
The trajectories of particles in Stokes waves. Zbl 1108.76013
2006
Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044
2006
Integrability of invariant metrics on the diffeomorphism group of the circle. Zbl 1170.37336
Constantin, A.; Kolev, B.
2006
Global existence for fully parabolic boundary value problems. Zbl 1108.35091
2006
Integrability of invariant metrics on the Virasoro group. Zbl 1195.58006
Constantin, A.; Kolev, B.; Lenells, J.
2006
Poisson structure and action-angle variables for the Camassa-Holm equation. Zbl 1137.37032
2006
Finite propagation speed for the Camassa-Holm equation. Zbl 1076.35109
2005
Global solutions of the Hunter–Saxton equation. Zbl 1108.35024
2005
On the existence of positive solutions of second order differential equations. Zbl 1223.34041
2005
A Hamiltonian formulation for free surface water waves with non-vanishing vorticity. Zbl 1362.35219
2005
Global existence for parabolic systems by Lyapunov functions. Zbl 1103.35035
2005
Wave-current interactions. Zbl 1331.76028
2005
Exact steady periodic water waves with vorticity. Zbl 1038.76011
2004
Symmetry of steady periodic surface water waves with vorticity. Zbl 1050.76007
2004
Symmetry of steady deep-water waves with vorticity. Zbl 1125.76007
2004
Global solutions for quasilinear parabolic systems. Zbl 1043.35066
Constantin, Adrian; Escher, Joachim; Yin, Zhaoyang
2004
Wave motion. Zbl 1077.76508
Constantin, Adrian (ed.); Escher, Joachim (ed.)
2004
Geodesic flow on the diffeomorphism group of the circle. Zbl 1037.37032
2003
On the inverse scattering approach to the Camassa-Holm equation. Zbl 1038.35067
2003
On the inverse scattering approach for an integrable shallow water wave equation. Zbl 1010.76011
2003
$$H^k$$ metrics on the diffeomorphism group of the circle. Zbl 1043.58004
2003
Stability of the Camassa-Holm solitons. Zbl 1022.35053
Constantin, A.; Strauss, W. A.
2002
On the geometric approach to the motion of inertial mechanical systems. Zbl 1039.37068
2002
Exact periodic traveling water waves with vorticity. Zbl 1020.35012
2002
The initial value problem for a generalized Boussinesq equation. Zbl 1161.35445
2002
Global solutions for quasilinear parabolic problems. Zbl 1004.35070
2002
On the scattering problem for the Camassa-Holm equation. Zbl 0999.35065
2001
On the deep water wave motion. Zbl 0982.76015
2001
Edge waves along a sloping beach. Zbl 1005.76009
2001
Orbital stability of solitary waves for a shallow water equation. Zbl 0984.35139
2001
Least action principle for an integrable shallow water equation. Zbl 0992.35088
2001
A Lagrangian approximation to the water-wave problem. Zbl 0985.35069
Constantin, A.
2001
The construction of an evolution system in the hyperbolic case and applications. Zbl 0982.35072
2001
Geometrical methods in hydrodynamics. Zbl 1007.35086
2001
Stability of peakons. Zbl 1049.35149
2000
Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Zbl 0944.35062
2000
Global weak solutions for a shallow water equation. Zbl 1002.35101
2000
On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Zbl 0954.35136
2000
...and 54 more Documents
all top 5

#### Cited by 1,508 Authors

 101 Yin, Zhaoyang 68 Constantin, Adrian 48 Liu, Yue 38 Martin, Calin-Iulian 38 Qiao, Zhijun 34 Escher, Joachim 33 Tian, Lixin 30 Mu, Chunlai 28 Lai, Shaoyong 27 Liu, Zhengrong 27 Qu, Changzheng 27 Zhou, Shouming 26 Ionescu-Kruse, Delia 26 Mi, Yongsheng 25 Guo, Zhengguang 25 Lenells, Jonatan 24 Mustafa, Octavian G. 23 Hsu, Hung-Chu 22 Ehrnström, Mats 21 Himonas, A. Alexandrou 20 Ivanov, Rossen I. 19 Guo, Boling 19 Liu, Xingxing 18 Henry, David 18 Kolev, Boris 18 Li, Yongsheng 18 Matioc, Bogdan-Vasile 17 Chen, Robin Ming 17 Gao, Hongjun 17 Holden, Helge 17 Yan, Wei 15 Raynaud, Xavier 15 Yan, Kai 15 Zhou, Yong 15 Zhu, Min 14 Fu, Ying 14 Gui, Guilong 14 Henry, David 14 Hur, Vera Mikyoung 14 Strauss, Walter Alexander 14 Wahlén, Erik 13 Guan, Chunxia 13 Hu, Qiaoyi 13 Shen, Chunyu 12 Basu, Biswajit 12 Chu, Jifeng 12 Guo, Fei 12 Guo, Yunxi 12 Matioc, Anca-Voichita 11 Geyer, Anna 11 Kalisch, Henrik 11 Moon, Byungsoo 11 Wu, Xinglong 10 Bauer, Martin 10 Erbay, Husnuata A. 10 Erkip, Albert Kohen 10 Fan, Lili 10 Grunert, Katrin 10 Lyons, Tony 10 Preston, Stephen C. 10 Walsh, Samuel 10 Wu, Yonghong 10 Zhu, Mingxuan 9 Boutet de Monvel, Anne Marie 9 Bressan, Alberto 9 Gasull, Armengol 9 Jiang, Zaihong 9 Li, Jinlu 9 Liu, Jingjing 9 Liu, Xiaochuan 9 Long, Yao 9 Lv, Guangying 9 Ma, Ruyun 9 Ni, Lidiao 9 Rui, Weiguo 9 Shepelsky, Dmitry 9 Wunsch, Marcus 8 Bruveris, Martins 8 Clamond, Didier 8 Coclite, Giuseppe Maria 8 Ding, Danping 8 Eckhardt, Jonathan 8 Erbay, Saadet 8 He, Bin 8 Kogelbauer, Florian 8 Novruzov, Emil B. 8 Quirchmayr, Ronald 8 Stuhlmeier, Raphael 8 Szmigielski, Jacek 8 Tang, Hao 8 Wang, Yujuan 8 Wheeler, Miles H. 8 Zong, Xiju 7 Anco, Stephen C. 7 Chang, Xiangke 7 Chen, Geng 7 Chen, Yong 7 Duruk Mutlubaş, Nilay 7 Jin, Liangbing 7 Johnson, Robin Stanley ...and 1,408 more Authors
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#### Cited in 241 Serials

 159 Journal of Differential Equations 138 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 92 Discrete and Continuous Dynamical Systems 88 Journal of Nonlinear Mathematical Physics 87 Journal of Mathematical Analysis and Applications 82 Journal of Mathematical Physics 78 Nonlinear Analysis. Real World Applications 74 Monatshefte für Mathematik 54 Applicable Analysis 48 Journal of Mathematical Fluid Mechanics 43 Journal of Fluid Mechanics 39 Abstract and Applied Analysis 35 Applied Mathematics and Computation 32 Archive for Rational Mechanics and Analysis 27 Boundary Value Problems 23 Communications in Mathematical Physics 22 Applied Mathematics Letters 21 Wave Motion 21 Journal of Functional Analysis 21 European Journal of Mechanics. B. Fluids 18 Annali di Matematica Pura ed Applicata. Serie Quarta 18 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 18 Journal of Nonlinear Science 17 Communications in Partial Differential Equations 17 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 15 Chaos, Solitons and Fractals 14 Journal of Evolution Equations 13 Quarterly of Applied Mathematics 13 Physica D 12 Theoretical and Mathematical Physics 12 Advances in Mathematics 11 Mathematical Methods in the Applied Sciences 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Journal of Geometry and Physics 11 Journal of Computational and Applied Mathematics 11 Journal of Inequalities and Applications 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Advances in Mathematical Physics 10 Mathematische Annalen 9 Letters in Mathematical Physics 9 Physics Letters. A 9 Journal of Hyperbolic Differential Equations 8 Communications on Pure and Applied Mathematics 8 Nonlinearity 8 Proceedings of the American Mathematical Society 8 Studies in Applied Mathematics 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Mathematical Problems in Engineering 8 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 8 Communications in Nonlinear Science and Numerical Simulation 7 Applied Numerical Mathematics 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 SIAM Journal on Mathematical Analysis 7 NoDEA. Nonlinear Differential Equations and Applications 7 Journal of Applied Mathematics 6 Journal of Computational Physics 6 Calculus of Variations and Partial Differential Equations 6 Mathematical Physics, Analysis and Geometry 6 Advances in Difference Equations 6 Analysis and Mathematical Physics 5 Computers & Mathematics with Applications 5 Annales de l’Institut Fourier 5 Inventiones Mathematicae 5 Mathematische Nachrichten 5 Mathematische Zeitschrift 5 Annals of Global Analysis and Geometry 5 Journal of Dynamics and Differential Equations 5 Discrete and Continuous Dynamical Systems. Series B 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Discrete and Continuous Dynamical Systems. Series S 5 Electronic Research Archive 4 Bulletin of the Australian Mathematical Society 4 Reviews in Mathematical Physics 4 Mathematics and Computers in Simulation 4 Acta Applicandae Mathematicae 4 Electronic Journal of Differential Equations (EJDE) 4 Acta Mathematica Sinica. English Series 4 Communications on Pure and Applied Analysis 4 Communications in Theoretical Physics 4 Water Waves 3 Journal of Engineering Mathematics 3 Acta Mathematica 3 Glasgow Mathematical Journal 3 Numerische Mathematik 3 Results in Mathematics 3 Zeitschrift für Analysis und ihre Anwendungen 3 Acta Mathematicae Applicatae Sinica. English Series 3 Japan Journal of Industrial and Applied Mathematics 3 Journal of Inverse and Ill-Posed Problems 3 Nonlinear Dynamics 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Differential Equations 3 Advanced Nonlinear Studies 3 Journal of Applied Mathematics and Computing 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Analysis and Applications (Singapore) 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Frontiers of Mathematics in China 3 Journal of Geometric Mechanics 2 Computers and Fluids ...and 141 more Serials
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#### Cited in 48 Fields

 1,548 Partial differential equations (35-XX) 665 Fluid mechanics (76-XX) 367 Dynamical systems and ergodic theory (37-XX) 187 Ordinary differential equations (34-XX) 123 Geophysics (86-XX) 63 Numerical analysis (65-XX) 61 Global analysis, analysis on manifolds (58-XX) 54 Mechanics of deformable solids (74-XX) 45 Operator theory (47-XX) 31 Differential geometry (53-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 26 Functions of a complex variable (30-XX) 25 Integral equations (45-XX) 24 Systems theory; control (93-XX) 19 Real functions (26-XX) 19 Probability theory and stochastic processes (60-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 17 Mechanics of particles and systems (70-XX) 16 Potential theory (31-XX) 11 Difference and functional equations (39-XX) 11 Functional analysis (46-XX) 11 General topology (54-XX) 10 Manifolds and cell complexes (57-XX) 10 Quantum theory (81-XX) 9 Group theory and generalizations (20-XX) 9 Topological groups, Lie groups (22-XX) 7 Nonassociative rings and algebras (17-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Optics, electromagnetic theory (78-XX) 5 Biology and other natural sciences (92-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Integral transforms, operational calculus (44-XX) 4 Operations research, mathematical programming (90-XX) 3 Algebraic geometry (14-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Relativity and gravitational theory (83-XX) 2 Field theory and polynomials (12-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 $$K$$-theory (19-XX) 1 Convex and discrete geometry (52-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

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