Edit Profile (opens in new tab) Rybkin, Alexei Compute Distance To: Compute Author ID: rybkin.alexei Published as: Rybkin, Alexei Documents Indexed: 36 Publications since 1999 Co-Authors: 12 Co-Authors with 13 Joint Publications 215 Co-Co-Authors all top 5 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 all top 5 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 all top 5 Fields 20 Partial differential equations (35-XX) 17 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 27 Publications have been cited 134 times in 78 Documents Cited by ▼ Year ▼ The boundary control approach to the Titchmarsh-Weyl \(m\)-function. I: The response operator and the \(A\)-amplitude. Zbl 1140.93023Avdonin, 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 1229.49026Rybkin, Alexei 12 2011 Soliton theory and Hankel operators. Zbl 1332.35325Grudsky, Sergei; Rybkin, Alexei 11 2015 Some new and old asymptotic representations of the Jost solution and the Weyl \(m\)-function for Schrödinger operators on the line. Zbl 1048.34140Rybkin, Alexei 9 2002 Spatial analyticity of solutions to integrable systems. I. The KdV case. Zbl 1387.37065Rybkin, Alexei 9 2013 Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line. Zbl 1188.37068Rybkin, Alexei 8 2010 On positive type initial profiles for the KdV equation. Zbl 1294.35122Grudsky, Sergei; Rybkin, Alexei 7 2014 Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier-Greenspan approach. Zbl 1416.86007Rybkin, Alexei; Pelinovsky, Efim; Didenkulova, Ira 6 2014 KdV equation beyond standard assumptions on initial data. Zbl 1380.35138Rybkin, Alexei 6 2018 On the evolution of a reflection coefficient under the Korteweg-de Vries flow. Zbl 1152.81597Rybkin, Alexei 6 2008 On classical solutions of the KdV equation. Zbl 1448.35444Grudsky, Sergei; Rybkin, Alexei 5 2020 On the trace approach to the inverse scattering problem in dimension one. Zbl 0988.34068Rybkin, Alexei 5 2001 Regularized perturbation determinants and KdV conservation laws for irregular initial profiles. Zbl 1191.35235Rybkin, Alexei 5 2010 The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles. Zbl 1328.35199Grudsky, Sergei; Remling, Christian; Rybkin, Alexei 4 2015 On the spectral \(L_{2}\) conjecture, \(3/2\)-Lieb-Thirring inequality and distributional potentials. Zbl 1111.81063Rybkin, Alexei 4 2005 On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. Zbl 0986.34073Rybkin, Alexei 3 2002 A new interpolation formula for the Titchmarsh-Weyl \(m\)-function. Zbl 1180.47033Rybkin, Alexei; Tuan, Vu Kim 3 2009 KdV invariants and Herglotz functions. Zbl 1034.35124Rybkin, Alexei 3 2001 Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations. Zbl 1412.35198Rybkin, Alexei 2 2019 On a trace formula of the Buslaev-Faddeev type for a long-range potential. Zbl 0952.34069Rybkin, Alexei 2 1999 On the existence of WKB-type asymptotics for the generalized eigenvectors of discrete string operators. Zbl 1063.47022Belov, Sergei; Rybkin, Alexei 2 2004 On Toeplitz and Hankel operators with oscillatory symbols containing Blaschke products and applications to the KdV equation. Zbl 1275.47059Grudsky, Sergei; Rybkin, Alexei 2 2013 On the absolutely continuous and negative discrete spectra of Schrödinger operators on the line with locally integrable globally square summable potentials. Zbl 1068.81024Rybkin, Alexei 2 2004 On the transformation of the Sturm-Liouville equation with slowly decaying potentials and the Titchmarsh-Weyl \(m\)-function. Zbl 1073.34022Rybkin, Alexei 2 2004 Preservation of the absolutely continuous spectrum: some extensions of a result by Molchanov-Novitskii-Vainberg. Zbl 1116.34064Rybkin, Alexei 1 2006 On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions. Zbl 1427.35243Rybkin, Alexei 1 2018 The generalized Carrier-Greenspan transform for the shallow water system with arbitrary initial and boundary conditions. Zbl 1477.35177Rybkin, Alexei; Nicolsky, Dmitry; Pelinovsky, Efim; Buckel, Maxwell 1 2021 The generalized Carrier-Greenspan transform for the shallow water system with arbitrary initial and boundary conditions. Zbl 1477.35177Rybkin, Alexei; Nicolsky, Dmitry; Pelinovsky, Efim; Buckel, Maxwell 1 2021 On classical solutions of the KdV equation. Zbl 1448.35444Grudsky, Sergei; Rybkin, Alexei 5 2020 Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations. Zbl 1412.35198Rybkin, Alexei 2 2019 KdV equation beyond standard assumptions on initial data. Zbl 1380.35138Rybkin, Alexei 6 2018 On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions. Zbl 1427.35243Rybkin, Alexei 1 2018 Soliton theory and Hankel operators. Zbl 1332.35325Grudsky, Sergei; Rybkin, Alexei 11 2015 The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles. Zbl 1328.35199Grudsky, Sergei; Remling, Christian; Rybkin, Alexei 4 2015 On positive type initial profiles for the KdV equation. Zbl 1294.35122Grudsky, Sergei; Rybkin, Alexei 7 2014 Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier-Greenspan approach. Zbl 1416.86007Rybkin, Alexei; Pelinovsky, Efim; Didenkulova, Ira 6 2014 Spatial analyticity of solutions to integrable systems. I. The KdV case. Zbl 1387.37065Rybkin, Alexei 9 2013 On Toeplitz and Hankel operators with oscillatory symbols containing Blaschke products and applications to the KdV equation. Zbl 1275.47059Grudsky, 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 1229.49026Rybkin, Alexei 12 2011 Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line. Zbl 1188.37068Rybkin, Alexei 8 2010 Regularized perturbation determinants and KdV conservation laws for irregular initial profiles. Zbl 1191.35235Rybkin, Alexei 5 2010 A new interpolation formula for the Titchmarsh-Weyl \(m\)-function. Zbl 1180.47033Rybkin, Alexei; Tuan, Vu Kim 3 2009 On the evolution of a reflection coefficient under the Korteweg-de Vries flow. Zbl 1152.81597Rybkin, Alexei 6 2008 The boundary control approach to the Titchmarsh-Weyl \(m\)-function. I: The response operator and the \(A\)-amplitude. Zbl 1140.93023Avdonin, Sergei; Mikhaylov, Victor; Rybkin, Alexei 13 2007 Preservation of the absolutely continuous spectrum: some extensions of a result by Molchanov-Novitskii-Vainberg. Zbl 1116.34064Rybkin, Alexei 1 2006 On the spectral \(L_{2}\) conjecture, \(3/2\)-Lieb-Thirring inequality and distributional potentials. Zbl 1111.81063Rybkin, Alexei 4 2005 On the existence of WKB-type asymptotics for the generalized eigenvectors of discrete string operators. Zbl 1063.47022Belov, 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 1068.81024Rybkin, Alexei 2 2004 On the transformation of the Sturm-Liouville equation with slowly decaying potentials and the Titchmarsh-Weyl \(m\)-function. Zbl 1073.34022Rybkin, 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 1048.34140Rybkin, Alexei 9 2002 On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials. Zbl 0986.34073Rybkin, Alexei 3 2002 On the trace approach to the inverse scattering problem in dimension one. Zbl 0988.34068Rybkin, Alexei 5 2001 KdV invariants and Herglotz functions. Zbl 1034.35124Rybkin, Alexei 3 2001 On a trace formula of the Buslaev-Faddeev type for a long-range potential. Zbl 0952.34069Rybkin, Alexei 2 1999 all cited Publications top 5 cited Publications all top 5 Cited by 99 Authors 13 Rybkin, Alexei 6 Mikhaylov, Victor S. 5 Avdonin, Sergeĭ Anatol’evich 5 Remling, Christian 4 Grudsky, Sergei Mikhailovich 4 Killip, Rowan 4 Teschl, Gerald 3 Egorova, Iryna 3 Gesztesy, Fritz 3 Sakhnovich, Alexander L. 3 Visan, Monica 3 Vu Kim Tuan 2 Bell, Jonathan 2 Damanik, David 2 Eckhardt, Jonathan 2 Kostenko, Aleksey S. 2 Laurens, Thierry 2 Li, Ze 2 Lukic, Milivoje 2 Malham, Simon J. A. 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 Domrin, Andrei Victorovich 1 Fritzsche, Bernd 1 Fucci, Guglielmo 1 Garayshin, V. V. 1 Gilbert, Daphne J. 1 Goldstein, Michael 1 Guyenne, Philippe 1 Harris, Bernard J. 1 Harris, Matthew W. 1 Huang, Jianhua 1 Janas, Jan 1 Kirstein, Bernd 1 Kirsten, Klaus 1 Kukuljan, Teo 1 Kurasov, Pavel B. 1 Lange, Till Luc 1 Laptev, Ari 1 Leugering, Günter 1 Lotoreichik, Vladimir 1 Luger, Annemarie 1 Malamud, Mark M. 1 Marletta, Marco 1 Matskevich, N. A. 1 Michor, Johanna 1 Moszyński, Marcin 1 Naboko, Serguei N. 1 Neidhardt, Hagen 1 Newsham, Samantha L. 1 Nguyen Thanh Hong 1 Nicholls, David P. 1 Nicolsky, D. J. 1 Nicolsky, Dmitry 1 Nurtazina, K. B. 1 Nurtazina, Karlygash 1 Ong, Darren C. 1 Pelinovskiĭ, Efim Naumovich 1 Pelinovsky, Efim 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 Sulem, Catherine 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 45 Serials 5 Communications in Mathematical Physics 5 Journal of Mathematical Physics 5 Proceedings of the American Mathematical Society 4 Nonlinearity 3 Journal of Mathematical Analysis and Applications 3 Journal of Differential Equations 3 Journal of Functional Analysis 3 Physica D 3 Journal of Mathematical Sciences (New York) 2 Journal d’Analyse Mathématique 2 Duke Mathematical Journal 2 Transactions of the American Mathematical Society 2 SIAM Journal on Mathematical Analysis 2 Annals of Mathematics. Second Series 2 Water Waves 1 Israel Journal of Mathematics 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 Transactions of the Moscow Mathematical Society 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 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 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 all top 5 Cited in 23 Fields 41 Partial differential equations (35-XX) 30 Ordinary differential equations (34-XX) 21 Operator theory (47-XX) 19 Dynamical systems and ergodic theory (37-XX) 12 Quantum theory (81-XX) 6 Fluid mechanics (76-XX) 5 Systems theory; control (93-XX) 4 Difference and functional equations (39-XX) 3 Combinatorics (05-XX) 3 Functions of a complex variable (30-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Geophysics (86-XX) 2 History and biography (01-XX) 2 Integral equations (45-XX) 2 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) Citations by Year