## Rybkin, Alexei

Compute Distance To:
 Author ID: 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
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### Co-Authors

 23 single-authored 6 Grudsky, Sergei Mikhailovich 2 Bastille, Odile 2 Pelinovsky, Efim 1 Avdonin, Sergeĭ Anatol’evich 1 Baggett, Jason 1 Belov, Sergei A. 1 Buckel, Maxwell 1 Didenkulova, Ira 1 Mikhaylov, Victor S. 1 Nicolsky, Dmitry 1 Remling, Christian 1 Vu Kim Tuan
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### Serials

 5 Journal of Mathematical Physics 5 Proceedings of the American Mathematical Society 4 Nonlinearity 2 Inverse Problems 2 Bulletin of the London Mathematical Society 2 SIAM Journal on Mathematical Analysis 1 Communications in Mathematical Physics 1 Journal of Fluid Mechanics 1 Proceedings of the London Mathematical Society. Third Series 1 Complex Variables. Theory and Application 1 Physica D 1 Applied Mathematics Letters 1 Differential and Integral Equations 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Electronic Journal of Differential Equations (EJDE) 1 Inverse Problems and Imaging 1 Water Waves
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### Fields

 19 Partial differential equations (35-XX) 18 Ordinary differential equations (34-XX) 15 Operator theory (47-XX) 13 Dynamical systems and ergodic theory (37-XX) 8 Quantum theory (81-XX) 3 Functions of a complex variable (30-XX) 2 Numerical analysis (65-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX)

### 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
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
2011
Soliton theory and Hankel operators. Zbl 1332.35325
Grudsky, Sergei; Rybkin, Alexei
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
2002
Spatial analyticity of solutions to integrable systems. I. The KdV case. Zbl 1387.37065
Rybkin, Alexei
2013
Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line. Zbl 1188.37068
Rybkin, Alexei
2010
On the evolution of a reflection coefficient under the Korteweg-de Vries flow. Zbl 1152.81597
Rybkin, Alexei
2008
On positive type initial profiles for the KdV equation. Zbl 1294.35122
Grudsky, Sergei; Rybkin, Alexei
2014
Regularized perturbation determinants and KdV conservation laws for irregular initial profiles. Zbl 1191.35235
Rybkin, Alexei
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
2014
KdV equation beyond standard assumptions on initial data. Zbl 1380.35138
Rybkin, Alexei
2018
On the trace approach to the inverse scattering problem in dimension one. Zbl 0988.34068
Rybkin, Alexei
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
2015
KdV invariants and Herglotz functions. Zbl 1034.35124
Rybkin, Alexei
2001
On the spectral $$L_{2}$$ conjecture, $$3/2$$-Lieb-Thirring inequality and distributional potentials. Zbl 1111.81063
Rybkin, Alexei
2005
A new interpolation formula for the Titchmarsh-Weyl $$m$$-function. Zbl 1180.47033
Rybkin, Alexei; Tuan, Vu Kim
2009
On classical solutions of the KdV equation. Zbl 1448.35444
Grudsky, Sergei; Rybkin, Alexei
2020
On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. Zbl 0986.34073
Rybkin, Alexei
2002
On a trace formula of the Buslaev-Faddeev type for a long-range potential. Zbl 0952.34069
Rybkin, Alexei
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
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
2013
On the existence of WKB-type asymptotics for the generalized eigenvectors of discrete string operators. Zbl 1063.47022
Belov, Sergei; Rybkin, Alexei
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
2004
On the transformation of the Sturm-Liouville equation with slowly decaying potentials and the Titchmarsh-Weyl $$m$$-function. Zbl 1073.34022
Rybkin, Alexei
2004
On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions. Zbl 1427.35243
Rybkin, Alexei
2018
On classical solutions of the KdV equation. Zbl 1448.35444
Grudsky, Sergei; Rybkin, Alexei
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
2019
KdV equation beyond standard assumptions on initial data. Zbl 1380.35138
Rybkin, Alexei
2018
On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions. Zbl 1427.35243
Rybkin, Alexei
2018
Soliton theory and Hankel operators. Zbl 1332.35325
Grudsky, Sergei; Rybkin, Alexei
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
2015
On positive type initial profiles for the KdV equation. Zbl 1294.35122
Grudsky, Sergei; Rybkin, Alexei
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
2014
Spatial analyticity of solutions to integrable systems. I. The KdV case. Zbl 1387.37065
Rybkin, Alexei
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
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
2011
Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line. Zbl 1188.37068
Rybkin, Alexei
2010
Regularized perturbation determinants and KdV conservation laws for irregular initial profiles. Zbl 1191.35235
Rybkin, Alexei
2010
A new interpolation formula for the Titchmarsh-Weyl $$m$$-function. Zbl 1180.47033
Rybkin, Alexei; Tuan, Vu Kim
2009
On the evolution of a reflection coefficient under the Korteweg-de Vries flow. Zbl 1152.81597
Rybkin, Alexei
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
2007
On the spectral $$L_{2}$$ conjecture, $$3/2$$-Lieb-Thirring inequality and distributional potentials. Zbl 1111.81063
Rybkin, Alexei
2005
On the existence of WKB-type asymptotics for the generalized eigenvectors of discrete string operators. Zbl 1063.47022
Belov, Sergei; Rybkin, Alexei
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
2004
On the transformation of the Sturm-Liouville equation with slowly decaying potentials and the Titchmarsh-Weyl $$m$$-function. Zbl 1073.34022
Rybkin, Alexei
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
2002
On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. Zbl 0986.34073
Rybkin, Alexei
2002
On the trace approach to the inverse scattering problem in dimension one. Zbl 0988.34068
Rybkin, Alexei
2001
KdV invariants and Herglotz functions. Zbl 1034.35124
Rybkin, Alexei
2001
On a trace formula of the Buslaev-Faddeev type for a long-range potential. Zbl 0952.34069
Rybkin, Alexei
1999
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### 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
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### 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
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### Cited in 21 Fields

 36 Partial differential equations (35-XX) 29 Ordinary differential equations (34-XX) 21 Operator theory (47-XX) 16 Dynamical systems and ergodic theory (37-XX) 12 Quantum theory (81-XX) 5 Systems theory; control (93-XX) 4 Difference and functional equations (39-XX) 4 Fluid mechanics (76-XX) 3 Combinatorics (05-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Functions of a complex variable (30-XX) 2 Numerical analysis (65-XX) 2 Geophysics (86-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX)