Figueira, Renata O.; Himonas, A. Alexandrou Lower bounds on the radius of analyticity for a system of modified KdV equations. (English) Zbl 1462.35333 J. Math. Anal. Appl. 497, No. 2, Article ID 124917, 17 p. (2021). MSC: 35Q53 35A01 35A02 PDF BibTeX XML Cite \textit{R. O. Figueira} and \textit{A. A. Himonas}, J. Math. Anal. Appl. 497, No. 2, Article ID 124917, 17 p. (2021; Zbl 1462.35333) Full Text: DOI OpenURL
Carillo, Sandra; Schiavo, Mauro Lo; Schiebold, Cornelia Abelian versus non-abelian Bäcklund charts: some remarks. (English) Zbl 1426.58010 Evol. Equ. Control Theory 8, No. 1, 43-55 (2019). MSC: 58J72 35Q53 35A30 PDF BibTeX XML Cite \textit{S. Carillo} et al., Evol. Equ. Control Theory 8, No. 1, 43--55 (2019; Zbl 1426.58010) Full Text: DOI arXiv OpenURL
Olver, Peter J.; Tsatis, Efstratios Points of constancy of the periodic linearized Korteweg-deVries equation. (English) Zbl 1407.35179 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2217, Article ID 20180160, 19 p. (2018). MSC: 35Q53 35B10 11J04 PDF BibTeX XML Cite \textit{P. J. Olver} and \textit{E. Tsatis}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2217, Article ID 20180160, 19 p. (2018; Zbl 1407.35179) Full Text: DOI arXiv OpenURL
Zarmi, Yair Soliton-generating \(\tau\)-functions revisited. (English) Zbl 1406.35323 J. Math. Phys. 59, No. 12, 122701, 21 p. (2018). MSC: 35Q51 35Q53 37K40 35C08 37K15 PDF BibTeX XML Cite \textit{Y. Zarmi}, J. Math. Phys. 59, No. 12, 122701, 21 p. (2018; Zbl 1406.35323) Full Text: DOI arXiv OpenURL
Zhao, Xiucheng; Huang, Langyang A compact difference scheme for the KdV equation. (Chinese. English summary) Zbl 1349.65360 Chin. J. Eng. Math. 32, No. 6, 876-882 (2015). MSC: 65M06 65M12 35Q53 65M15 PDF BibTeX XML Cite \textit{X. Zhao} and \textit{L. Huang}, Chin. J. Eng. Math. 32, No. 6, 876--882 (2015; Zbl 1349.65360) Full Text: DOI OpenURL
Toro, Eleuterio F.; Montecinos, Gino I. Advection-diffusion-reaction equations: hyperbolization and high-order ADER discretizations. (English) Zbl 1307.65117 SIAM J. Sci. Comput. 36, No. 5, A2423-A2457 (2014). MSC: 65M08 35Q53 35K57 65M12 PDF BibTeX XML Cite \textit{E. F. Toro} and \textit{G. I. Montecinos}, SIAM J. Sci. Comput. 36, No. 5, A2423--A2457 (2014; Zbl 1307.65117) Full Text: DOI OpenURL
Lassas, M.; Mueller, J. L.; Siltanen, S.; Stahel, A. The Novikov-Veselov equation and the inverse scattering method. II: Computation. (English) Zbl 1247.65116 Nonlinearity 25, No. 6, 1799-1818 (2012). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65M06 35Q53 47J35 37K15 65T60 PDF BibTeX XML Cite \textit{M. Lassas} et al., Nonlinearity 25, No. 6, 1799--1818 (2012; Zbl 1247.65116) Full Text: DOI OpenURL
Álvarez, J.; Durán, A. On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations. (English) Zbl 1247.65122 Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 637-649 (2012). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65M20 35Q53 35L75 65M15 PDF BibTeX XML Cite \textit{J. Álvarez} and \textit{A. Durán}, Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 637--649 (2012; Zbl 1247.65122) Full Text: DOI OpenURL
Djordjevic, Vladan D.; Atanackovic, Teodor M. Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations. (English) Zbl 1157.35470 J. Comput. Appl. Math. 222, No. 2, 701-714 (2008). MSC: 35Q53 35A30 35C05 35C20 PDF BibTeX XML Cite \textit{V. D. Djordjevic} and \textit{T. M. Atanackovic}, J. Comput. Appl. Math. 222, No. 2, 701--714 (2008; Zbl 1157.35470) Full Text: DOI OpenURL
Espinosa-Cerón, A.; Fujioka, J.; Malomed, B. A.; Rodríguez, R. F. Soliton dynamics in the complex modified KdV equation with a periodic potential. (English) Zbl 1163.35031 Physica D 236, No. 2, 141-151 (2007). Reviewer: Jochen Denzler (Knoxville) MSC: 35Q53 35Q51 35B35 35A15 PDF BibTeX XML Cite \textit{A. Espinosa-Cerón} et al., Physica D 236, No. 2, 141--151 (2007; Zbl 1163.35031) Full Text: DOI OpenURL
Levi, D. Multiple-scale analysis of discrete nonlinear partial difference equations: The reduction of the lattice potential KdV. (English) Zbl 1082.39013 J. Phys. A, Math. Gen. 38, No. 35, 7677-7689 (2005). Reviewer: Edwin Engin Yaz (Milwaukee) MSC: 39A12 37K60 37K10 37K40 35Q51 35Q53 PDF BibTeX XML Cite \textit{D. Levi}, J. Phys. A, Math. Gen. 38, No. 35, 7677--7689 (2005; Zbl 1082.39013) Full Text: DOI arXiv OpenURL
Syam, Muhammed I. Adomian decomposition method for approximating the solution of the Korteweg-deVries equation. (English) Zbl 1063.65112 Appl. Math. Comput. 162, No. 3, 1465-1473 (2005). MSC: 65M70 35Q53 PDF BibTeX XML Cite \textit{M. I. Syam}, Appl. Math. Comput. 162, No. 3, 1465--1473 (2005; Zbl 1063.65112) Full Text: DOI OpenURL
Christ, Michael; Colliander, James; Tao, Terrence Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations. (English) Zbl 1048.35101 Am. J. Math. 125, No. 6, 1235-1293 (2003). Reviewer: Alain Brillard (Mulhouse) MSC: 35Q53 35Q55 PDF BibTeX XML Cite \textit{M. Christ} et al., Am. J. Math. 125, No. 6, 1235--1293 (2003; Zbl 1048.35101) Full Text: DOI arXiv Link OpenURL
Sahadevan, R. Nonlinear differential-difference and difference equations: integrability and exact solvability. (English) Zbl 0996.35084 Comput. Math. Appl. 42, No. 3-5, 627-637 (2001). MSC: 35R10 39A12 37K10 PDF BibTeX XML Cite \textit{R. Sahadevan}, Comput. Math. Appl. 42, No. 3--5, 627--637 (2001; Zbl 0996.35084) Full Text: DOI OpenURL
Osman, E.-S.; Rida, S. Z. Multisoliton solution of a class of coupled soliton equations. (English) Zbl 0984.35137 Comput. Math. Appl. 41, No. 10-11, 1425-1430 (2001). MSC: 35Q51 35Q53 35C05 37K40 PDF BibTeX XML Cite \textit{E. S. Osman} and \textit{S. Z. Rida}, Comput. Math. Appl. 41, No. 10--11, 1425--1430 (2001; Zbl 0984.35137) Full Text: DOI OpenURL
Demiray, Hilmi The effect of shear stress on solitary waves in arteries. (English) Zbl 0892.92007 Bull. Math. Biol. 59, No. 5, 993-1012 (1997). MSC: 92C35 35Q53 76Z05 76B55 PDF BibTeX XML Cite \textit{H. Demiray}, Bull. Math. Biol. 59, No. 5, 993--1012 (1997; Zbl 0892.92007) Full Text: DOI OpenURL
Saichev, A. I.; Woyczynski, W. A. Density fields in Burgers and KdV-Burgers turbulence. (English) Zbl 0858.35112 SIAM J. Appl. Math. 56, No. 4, 1008-1038 (1996). MSC: 35Q53 60G60 76N15 76F99 PDF BibTeX XML Cite \textit{A. I. Saichev} and \textit{W. A. Woyczynski}, SIAM J. Appl. Math. 56, No. 4, 1008--1038 (1996; Zbl 0858.35112) Full Text: DOI OpenURL
Chen, Yunkai; Wen, Shih-Liang On existence theorems of periodic traveling wave solutions to the two- dimensional Korteweg-deVries equation. (English) Zbl 0639.35077 Appl. Anal. 31, No. 1-2, 1-10 (1988). Reviewer: Y.K.Chen MSC: 35Q99 35B10 35B40 35A05 PDF BibTeX XML Cite \textit{Y. Chen} and \textit{S.-L. Wen}, Appl. Anal. 31, No. 1--2, 1--10 (1988; Zbl 0639.35077) Full Text: DOI OpenURL
Benjamin, T. Brooke; Graham-Eagle, J. Long gravity-capillary waves with edge constraints. (English) Zbl 0584.76023 IMA J. Appl. Math. 35, 91-114 (1985). MSC: 76B15 76L05 PDF BibTeX XML Cite \textit{T. B. Benjamin} and \textit{J. Graham-Eagle}, IMA J. Appl. Math. 35, 91--114 (1985; Zbl 0584.76023) Full Text: DOI OpenURL
Debnath, L.; Shivamoggi, B. K. Some nonlinear model equations in dispersive systems and their solitary wave solutions in fluids and plasmas. (English) Zbl 0575.76030 Advances in nonlinear waves, Vol. II, Res. Notes Math. 111, 309-347 (1985). Reviewer: M.Biermann MSC: 76B25 76X05 PDF BibTeX XML OpenURL
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P. Modern geometry - methods and applications. Part 2: The geometry and topology of manifolds. Transl. from the Russian by Robert G. Burns. (English) Zbl 0565.57001 Graduate Texts in Mathematics, 104. New York etc.: Springer-Verlag. XV, 430 p. DM 158.00 (1985). MSC: 57-01 55-01 53-01 70G10 70H05 70Sxx 81T08 83F05 22E10 22E15 32Q99 53C05 53C20 53C22 53C30 53C35 53A05 55Q05 55Q15 55Q25 55M20 55M25 55Q40 55R05 55R10 55R25 55R40 57M05 57M10 57M25 57N80 57R20 57R30 57R35 57R70 57R25 37J99 37J35 37K10 37D40 53D25 58J35 58J45 58E30 PDF BibTeX XML OpenURL
Newell, Alan C. Solitons in mathematics and physics. (English) Zbl 0565.35003 CBMS-NSF Regional Conference Series in Applied Mathematics 48. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 0-89871-196-7). xvi, 246 p. (1985). Reviewer: Gui-Zhang Tu MSC: 35-02 35Q51 35Q53 35Q55 35A30 37K40 37K15 37K20 37K30 37K35 37K10 17B67 17B80 70H05 34L99 35P25 76B15 PDF BibTeX XML Cite \textit{A. C. Newell}, Solitons in mathematics and physics. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (1985; Zbl 0565.35003) OpenURL
Đorđević, Vladan D. Some exact solutions of the Korteweg-deVries equation with variable coefficients. (Croatian. English summary) Zbl 0565.35091 Zb. Rad., Nova Ser. 4(12), 61-66 (1984). MSC: 35Q99 35A30 35C05 PDF BibTeX XML Cite \textit{V. D. Đorđević}, Zb. Rad., Nova Ser. 4(12), 61--66 (1984; Zbl 0565.35091) OpenURL
Shen, M. C. Nonlinear capillary waves under gravity with edge constraints in a channel. (English) Zbl 0521.76020 Phys. Fluids 26, 1417-1421 (1983). MSC: 76B15 35Q99 PDF BibTeX XML Cite \textit{M. C. Shen}, Phys. Fluids 26, 1417--1421 (1983; Zbl 0521.76020) Full Text: DOI OpenURL
Achuthan, P. Solitons and nonlinear waves. (English) Zbl 0513.35023 Mathematics at the service of man, Proc. 2nd World Conf., Las Palmas/Spain 1982, 93-96 (1982). MSC: 35G20 35Q99 PDF BibTeX XML OpenURL
Buslaev, V. S.; Sukhanov, V. V. On the asymptotic behaviour for \(t\to \infty\) of the solutions of the equation \(\psi_{xx} + u(x,t) \psi + (\lambda/4) \psi = 0\) with a potential \(u\) satisfying the Korteweg-deVries equation. I. (Russian) Zbl 0513.35011 Probl. Mat. Fiz. 10, 70-102 (1982). MSC: 35B40 35Q99 34L99 PDF BibTeX XML Cite \textit{V. S. Buslaev} and \textit{V. V. Sukhanov}, Probl. Mat. Fiz. 10, 70--102 (1982; Zbl 0513.35011) OpenURL
Knoerrer, Horst Geodesics on quadrics and a mechanical problem of C. Neumann. (English) Zbl 0478.58014 J. Reine Angew. Math. 334, 69-78 (1982). MSC: 37J99 37D40 53D25 53C22 70H03 53A07 PDF BibTeX XML Cite \textit{H. Knoerrer}, J. Reine Angew. Math. 334, 69--78 (1982; Zbl 0478.58014) Full Text: DOI Crelle EuDML OpenURL
Grimshaw, R. Evolution equations for long, nonlinear internal waves in stratified shear flows. (English) Zbl 0492.76035 Stud. Appl. Math. 65, 159-188 (1981). MSC: 76B55 76V05 76F10 35Q99 PDF BibTeX XML Cite \textit{R. Grimshaw}, Stud. Appl. Math. 65, 159--188 (1981; Zbl 0492.76035) Full Text: DOI OpenURL
Koop, C. Gary; Butler, Gerald An investigation of internal solitary waves in a two-fluid system. (English) Zbl 0479.76036 J. Fluid Mech. 112, 225-251 (1981). MSC: 76B25 76B55 76-05 76D99 76E30 35Q99 PDF BibTeX XML Cite \textit{C. G. Koop} and \textit{G. Butler}, J. Fluid Mech. 112, 225--251 (1981; Zbl 0479.76036) Full Text: DOI OpenURL
Shadwick, W. F. The Hamilton Cartan formalism for rth-order Lagrangians and the integrability of the KdV and modified KdV equations. (English) Zbl 0473.58012 Lett. Math. Phys. 5, 137-141 (1981). MSC: 37J99 37J35 37K10 35Q99 49Q99 58A15 PDF BibTeX XML Cite \textit{W. F. Shadwick}, Lett. Math. Phys. 5, 137--141 (1981; Zbl 0473.58012) Full Text: DOI OpenURL
Gürses, Metin; Nutku, Yavuz New nonlinear evolution equations from surface theory. (English) Zbl 0471.35071 J. Math. Phys. 22, 1393-1398 (1981). MSC: 35Q99 35P25 53A05 PDF BibTeX XML Cite \textit{M. Gürses} and \textit{Y. Nutku}, J. Math. Phys. 22, 1393--1398 (1981; Zbl 0471.35071) Full Text: DOI Link OpenURL
Karney, Charles F. F. Temporal evolution of lower-hybrid waves in the presence of ponderomotive density fluctuations. (English) Zbl 0466.76129 Phys. Fluids 24, 127-138 (1981). MSC: 76X05 35Q99 PDF BibTeX XML Cite \textit{C. F. F. Karney}, Phys. Fluids 24, 127--138 (1981; Zbl 0466.76129) Full Text: DOI arXiv OpenURL
Eckhaus, Wiktor; van Harten, Aart The inverse scattering transformation and the theory of solitons. An introduction. (English) Zbl 0463.35001 North-Holland Mathematics Studies, 50. Amsterdam - New York -Oxford: North-Holland Publishing Company. XI, 222 p. $ 31.75; Dfl. 65.00 (1981). MSC: 35-02 35P25 35Q99 58D25 76B25 PDF BibTeX XML OpenURL
Krichever, I. M. Self-similar solutions of equations of Korteweg-deVries type. (English) Zbl 0454.35078 Funct. Anal. Appl. 14, 234-236 (1981). MSC: 35Q99 35P99 PDF BibTeX XML Cite \textit{I. M. Krichever}, Funct. Anal. Appl. 14, 234--236 (1981; Zbl 0454.35078) Full Text: DOI OpenURL
Moser, Jürgen Geometry of quadrics and spectral theory. (English) Zbl 0455.58018 Differential geometry, Proc. int. Chern Symp., Berkeley 1979, 147-188 (1980). MSC: 37J35 37K10 37J99 14H40 14H45 35Q99 PDF BibTeX XML OpenURL
Đorđević, Vladan D. On the simultaneous effect of viscosity and variable depth on the propagation of solitary waves. (English) Zbl 0454.76028 Int. J. Non-Linear Mech. 15, 443-447 (1980). MSC: 76B25 76B15 35Q99 PDF BibTeX XML Cite \textit{V. D. Đorđević}, Int. J. Non-Linear Mech. 15, 443--447 (1980; Zbl 0454.76028) Full Text: DOI OpenURL
Miura, Robert M. Explicit roots of the cubic polynomial and applications. (English) Zbl 0429.35058 Appl. Math. Notes 5, 22-40 (1980). MSC: 35Q99 35L05 35A25 30C10 26C10 34E20 PDF BibTeX XML Cite \textit{R. M. Miura}, Appl. Math. Notes 5, 22--40 (1980; Zbl 0429.35058) OpenURL
Adler, M. On a trace functional for formal pseudodifferential operators and the Hamiltonian structure of Korteweg-deVries type equations. (English) Zbl 0495.35072 Global analysis, Proc. bienn. Semin. Can. math. Congr., Calgary/ Alberta 1978, Lect. Notes Math. 755, 1-16 (1979). MSC: 35Q99 35A30 35S05 47F05 PDF BibTeX XML OpenURL
Chudnovsky, David V. Equations d’évolution opératorielles completement intégrables. (French) Zbl 0429.35047 C. R. Acad. Sci., Paris, Sér. A 289, 429-432 (1979). MSC: 35L60 47A50 35Q99 PDF BibTeX XML Cite \textit{D. V. Chudnovsky}, C. R. Acad. Sci., Paris, Sér. A 289, 429--432 (1979; Zbl 0429.35047) OpenURL
Pirani, F. A. E.; Robinson, D. C.; Shadwick, W. F. Local jet bundle formulation of Bäcklund transformations. With applications to non-linear evolution equations. (English) Zbl 0427.58003 Mathematical Physics Studies, Vol. 1, Dordrecht - Boston - London: D. Reidel Publishing Company. VIII, 132 p. Dfl. 22.50 (1979). MSC: 58A20 53B15 53C05 58Jxx PDF BibTeX XML OpenURL
Miles, John W. The asymptotic solution of the Korteweg-deVries equation in the absence of solitons. (English) Zbl 0412.35079 Stud. Appl. Math. 61, 59-72 (1979). MSC: 35Q99 35B40 PDF BibTeX XML Cite \textit{J. W. Miles}, Stud. Appl. Math. 61, 59--72 (1979; Zbl 0412.35079) Full Text: DOI OpenURL
Lax, Peter D.; Levermore, C. David The zero dispersion limit for the Korteweg-deVries KdV equation. (English) Zbl 0411.35081 Proc. Natl. Acad. Sci. USA 76, 3602-3606 (1979). MSC: 35Q99 35P25 35B40 78A45 90C20 PDF BibTeX XML Cite \textit{P. D. Lax} and \textit{C. D. Levermore}, Proc. Natl. Acad. Sci. USA 76, 3602--3606 (1979; Zbl 0411.35081) Full Text: DOI OpenURL
Adler, M. On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations. (English) Zbl 0393.35058 Invent. Math. 50, 219-248 (1979). MSC: 35Q99 35S99 70H99 PDF BibTeX XML Cite \textit{M. Adler}, Invent. Math. 50, 219--248 (1979; Zbl 0393.35058) Full Text: DOI EuDML OpenURL
Kruskal, M. The birth of the soliton. (English) Zbl 0425.35028 Nonlin. Evol. Equat. solv. by the Spectr. Transform, int. Symp., Rome 1977, Res. Notes Math. 26, 1-8 (1978). MSC: 35G20 35L65 76B25 35R25 35Q99 PDF BibTeX XML OpenURL