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Author ID: rybkin.alexei Recent zbMATH articles by "Rybkin, Alexei"
Published as: Rybkin, Alexei
Documents Indexed: 36 Publications since 1999
Co-Authors: 12 Co-Authors with 13 Joint Publications
210 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

25 Publications have been cited 122 times in 71 Documents Cited by Year
The boundary control approach to the Titchmarsh-Weyl \(m\)-function. I: The response operator and the \(A\)-amplitude. Zbl 1140.93023
Avdonin, Sergei; Mikhaylov, Victor; Rybkin, Alexei
13
2007
The Hirota \(\tau \)-function and well-posedness of the KdV equation with an arbitrary step-like initial profile decaying on the right half line. Zbl 1229.49026
Rybkin, Alexei
10
2011
Soliton theory and Hankel operators. Zbl 1332.35325
Grudsky, Sergei; Rybkin, Alexei
10
2015
Some new and old asymptotic representations of the Jost solution and the Weyl \(m\)-function for Schrödinger operators on the line. Zbl 1048.34140
Rybkin, Alexei
9
2002
Spatial analyticity of solutions to integrable systems. I. The KdV case. Zbl 1387.37065
Rybkin, Alexei
9
2013
Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line. Zbl 1188.37068
Rybkin, Alexei
8
2010
On the evolution of a reflection coefficient under the Korteweg-de Vries flow. Zbl 1152.81597
Rybkin, Alexei
6
2008
On positive type initial profiles for the KdV equation. Zbl 1294.35122
Grudsky, Sergei; Rybkin, Alexei
6
2014
Regularized perturbation determinants and KdV conservation laws for irregular initial profiles. Zbl 1191.35235
Rybkin, Alexei
5
2010
Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier-Greenspan approach. Zbl 1416.86007
Rybkin, Alexei; Pelinovsky, Efim; Didenkulova, Ira
5
2014
KdV equation beyond standard assumptions on initial data. Zbl 1380.35138
Rybkin, Alexei
5
2018
On the trace approach to the inverse scattering problem in dimension one. Zbl 0988.34068
Rybkin, Alexei
5
2001
The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles. Zbl 1328.35199
Grudsky, Sergei; Remling, Christian; Rybkin, Alexei
3
2015
KdV invariants and Herglotz functions. Zbl 1034.35124
Rybkin, Alexei
3
2001
On the spectral \(L_{2}\) conjecture, \(3/2\)-Lieb-Thirring inequality and distributional potentials. Zbl 1111.81063
Rybkin, Alexei
3
2005
A new interpolation formula for the Titchmarsh-Weyl \(m\)-function. Zbl 1180.47033
Rybkin, Alexei; Tuan, Vu Kim
3
2009
On classical solutions of the KdV equation. Zbl 1448.35444
Grudsky, Sergei; Rybkin, Alexei
3
2020
On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. Zbl 0986.34073
Rybkin, Alexei
3
2002
On a trace formula of the Buslaev-Faddeev type for a long-range potential. Zbl 0952.34069
Rybkin, Alexei
2
1999
Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations. Zbl 1412.35198
Rybkin, Alexei
2
2019
On Toeplitz and Hankel operators with oscillatory symbols containing Blaschke products and applications to the KdV equation. Zbl 1275.47059
Grudsky, Sergei; Rybkin, Alexei
2
2013
On the existence of WKB-type asymptotics for the generalized eigenvectors of discrete string operators. Zbl 1063.47022
Belov, Sergei; Rybkin, Alexei
2
2004
On the absolutely continuous and negative discrete spectra of Schrödinger operators on the line with locally integrable globally square summable potentials. Zbl 1068.81024
Rybkin, Alexei
2
2004
On the transformation of the Sturm-Liouville equation with slowly decaying potentials and the Titchmarsh-Weyl \(m\)-function. Zbl 1073.34022
Rybkin, Alexei
2
2004
On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions. Zbl 1427.35243
Rybkin, Alexei
1
2018
On classical solutions of the KdV equation. Zbl 1448.35444
Grudsky, Sergei; Rybkin, Alexei
3
2020
Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations. Zbl 1412.35198
Rybkin, Alexei
2
2019
KdV equation beyond standard assumptions on initial data. Zbl 1380.35138
Rybkin, Alexei
5
2018
On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions. Zbl 1427.35243
Rybkin, Alexei
1
2018
Soliton theory and Hankel operators. Zbl 1332.35325
Grudsky, Sergei; Rybkin, Alexei
10
2015
The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles. Zbl 1328.35199
Grudsky, Sergei; Remling, Christian; Rybkin, Alexei
3
2015
On positive type initial profiles for the KdV equation. Zbl 1294.35122
Grudsky, Sergei; Rybkin, Alexei
6
2014
Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier-Greenspan approach. Zbl 1416.86007
Rybkin, Alexei; Pelinovsky, Efim; Didenkulova, Ira
5
2014
Spatial analyticity of solutions to integrable systems. I. The KdV case. Zbl 1387.37065
Rybkin, Alexei
9
2013
On Toeplitz and Hankel operators with oscillatory symbols containing Blaschke products and applications to the KdV equation. Zbl 1275.47059
Grudsky, Sergei; Rybkin, Alexei
2
2013
The Hirota \(\tau \)-function and well-posedness of the KdV equation with an arbitrary step-like initial profile decaying on the right half line. Zbl 1229.49026
Rybkin, Alexei
10
2011
Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line. Zbl 1188.37068
Rybkin, Alexei
8
2010
Regularized perturbation determinants and KdV conservation laws for irregular initial profiles. Zbl 1191.35235
Rybkin, Alexei
5
2010
A new interpolation formula for the Titchmarsh-Weyl \(m\)-function. Zbl 1180.47033
Rybkin, Alexei; Tuan, Vu Kim
3
2009
On the evolution of a reflection coefficient under the Korteweg-de Vries flow. Zbl 1152.81597
Rybkin, Alexei
6
2008
The boundary control approach to the Titchmarsh-Weyl \(m\)-function. I: The response operator and the \(A\)-amplitude. Zbl 1140.93023
Avdonin, Sergei; Mikhaylov, Victor; Rybkin, Alexei
13
2007
On the spectral \(L_{2}\) conjecture, \(3/2\)-Lieb-Thirring inequality and distributional potentials. Zbl 1111.81063
Rybkin, Alexei
3
2005
On the existence of WKB-type asymptotics for the generalized eigenvectors of discrete string operators. Zbl 1063.47022
Belov, Sergei; Rybkin, Alexei
2
2004
On the absolutely continuous and negative discrete spectra of Schrödinger operators on the line with locally integrable globally square summable potentials. Zbl 1068.81024
Rybkin, Alexei
2
2004
On the transformation of the Sturm-Liouville equation with slowly decaying potentials and the Titchmarsh-Weyl \(m\)-function. Zbl 1073.34022
Rybkin, Alexei
2
2004
Some new and old asymptotic representations of the Jost solution and the Weyl \(m\)-function for Schrödinger operators on the line. Zbl 1048.34140
Rybkin, Alexei
9
2002
On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. Zbl 0986.34073
Rybkin, Alexei
3
2002
On the trace approach to the inverse scattering problem in dimension one. Zbl 0988.34068
Rybkin, Alexei
5
2001
KdV invariants and Herglotz functions. Zbl 1034.35124
Rybkin, Alexei
3
2001
On a trace formula of the Buslaev-Faddeev type for a long-range potential. Zbl 0952.34069
Rybkin, Alexei
2
1999
all top 5

Cited by 92 Authors

13 Rybkin, Alexei
6 Mikhaylov, Victor S.
5 Avdonin, Sergeĭ Anatol’evich
5 Remling, Christian
4 Grudsky, Sergei Mikhailovich
4 Killip, Rowan
3 Gesztesy, Fritz
3 Sakhnovich, Alexander L.
3 Teschl, Gerald
3 Visan, Monica
3 Vu Kim Tuan
2 Bell, Jonathan
2 Damanik, David
2 Egorova, Iryna
2 Li, Ze
2 Lukic, Milivoje
2 Mikhaylov, Alexander S.
2 Miyazawa, Toru
2 Rybkin, Alexey V.
2 Shimozono, Takenori
2 Wang, Ming
1 Abdon, Choque Rivero
1 Adler, Vsevolod Eduardovich
1 Andreiev, Kyrylo
1 Bilman, Deniz
1 Binder, Ilia A.
1 Bjørnestad, Maria
1 Blower, Gordon
1 Böttcher, Albrecht
1 Bouclet, Jean-Marc
1 Boumenir, Amin A.
1 Bringmann, Björn
1 Brown, Malcolm W.
1 Buckel, Maxwell
1 Clark, Steve
1 Comtet, Alain
1 Cornu, Françoise
1 Demirel, Semra
1 Didenko, Victor D.
1 Doikou, Anastasia
1 Eckhardt, Jonathan
1 Fritzsche, Bernd
1 Fucci, Guglielmo
1 Garayshin, V. V.
1 Gilbert, Daphne J.
1 Goldstein, Michael
1 Harris, Bernard J.
1 Harris, Matthew W.
1 Huang, Jianhua
1 Janas, Jan
1 Kirstein, Bernd
1 Kirsten, Klaus
1 Kostenko, Aleksey S.
1 Kurasov, Pavel B.
1 Lange, Till Luc
1 Laptev, Ari
1 Laurens, Thierry
1 Leugering, Günter
1 Lotoreichik, Vladimir
1 Luger, Annemarie
1 Malamud, Mark M.
1 Malham, Simon J. A.
1 Marletta, Marco
1 Moszyński, Marcin
1 Naboko, Serguei N.
1 Neidhardt, Hagen
1 Newsham, Samantha L.
1 Nguyen Thanh Hong
1 Nicolsky, D. J.
1 Nicolsky, Dmitry
1 Nurtazina, K. B.
1 Nurtazina, Karlygash
1 Ong, Darren C.
1 Pelinovsky, Efim
1 Pelinovsky, Efim N.
1 Riehl, Suzanne M.
1 Safronov, Oleg
1 Schehr, Grégory
1 Silbermann, Bernd
1 Simon, Barry
1 Simonov, Sergey A.
1 Stanfill, Jonathan
1 Stylianidis, Ioannis
1 Symons, Freddy
1 Tang, Xingdong
1 Tian, Bo
1 Trogdon, Thomas
1 Usman, Muhammad
1 Wöhrer, Tobias
1 Xu, Guixiang
1 Young, Giorgio
1 Yuditskii, Peter Meerovich
all top 5

Cited in 42 Serials

5 Journal of Mathematical Physics
5 Proceedings of the American Mathematical Society
4 Communications in Mathematical Physics
4 Nonlinearity
3 Journal of Differential Equations
3 Journal of Functional Analysis
3 Journal of Mathematical Sciences (New York)
2 Journal d’Analyse Mathématique
2 Journal of Mathematical Analysis and Applications
2 Duke Mathematical Journal
2 Transactions of the American Mathematical Society
2 Physica D
2 SIAM Journal on Mathematical Analysis
2 Annals of Mathematics. Second Series
1 Journal of Fluid Mechanics
1 Journal of Statistical Physics
1 Letters in Mathematical Physics
1 Mathematical Methods in the Applied Sciences
1 Mathematical Notes
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Reports on Mathematical Physics
1 Wave Motion
1 Advances in Mathematics
1 Applied Mathematics and Computation
1 Journal of the London Mathematical Society. Second Series
1 Monatshefte für Mathematik
1 Applied Mathematics Letters
1 Communications in Partial Differential Equations
1 Integral Transforms and Special Functions
1 Journal of Difference Equations and Applications
1 Boletín de la Sociedad Matemática Mexicana. Third Series
1 Mathematical Physics, Analysis and Geometry
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Annales Henri Poincaré
1 Journal of Nonlinear Mathematical Physics
1 Inverse Problems and Imaging
1 Mathematical Modelling of Natural Phenomena
1 Bulletin of Mathematical Sciences
1 Research in the Mathematical Sciences
1 Annals of PDE
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Water Waves

Citations by Year