Dmitry Shepelsky

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All published works

Action	Title	Year	Authors
+ PDF Chat	The integrable nonlocal nonlinear Schr\"odinger equation with oscillatory boundary conditions: long-time asymptotics	2025	Yan Rybalko Dmitry Shepelsky Shou‐Fu Tian
+	A Riemann–Hilbert approach to solution of the modified focusing complex short pulse equation	2024	Ruslan Barkov Dmitry Shepelsky
+	Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems	2024	Dmitry Shepelsky Iryna Karpenko Stepan Bogdanov Jaroslaw E. Prilepsky
+	Author response for "Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems"	2024	Dmitry Shepelsky Iryna Karpenko Stepan Bogdanov Jaroslaw E. Prilepsky
+ PDF Chat	Phase Computation for the Finite-Genus Solutions to the Focusing Nonlinear Schrödinger Equation Using Convolutional Neural Networks	2023	Stepan Bogdanov Dmitry Shepelsky Anastasiia Vasylchenkova Egor Sedov Pedro J. Freire Sergei K. Turitsyn Jaroslaw E. Prilepsky
+	Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Riemann-Hilbert approach: inverse and direct problems	2023	Dmitry Shepelsky Iryna Karpenko Stepan Bogdanov Jaroslaw E. Prilepsky
+ PDF Chat	Global conservative solutions of the nonlocal NLS equation beyond blow-up	2022	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	A Riemann–Hilbert approach to the modified Camassa–Holm equation with step-like boundary conditions	2022	Iryna Karpenko Dmitry Shepelsky Gerald Teschl
+	The Riemann-Hilbert problem approach to the short pulse equation	2022	Dmitry Shepelsky A Tiurdio Lech Zieliński
+ PDF Chat	The Focusing NLS Equation with Step-Like Oscillating Background: The Genus 3 Sector	2022	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+	Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behavior	2022	Anne Boutet de Monvel Yan Rybalko Dmitry Shepelsky
+	Global conservative solutions of the nonlocal NLS equation beyond blow-up	2022	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Focusing Nonlocal Nonlinear Schrödinger Equation with Asymmetric Boundary Conditions: Large-Time Behavior	2022	Anne Boutet de Monvel Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation	2021	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Asymptotic stage of modulation instability for the nonlocal nonlinear Schr\"odinger equation	2021	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Curved wedges in the long‐time asymptotics for the integrable nonlocal nonlinear Schrödinger equation	2021	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	The Focusing NLS Equation with Step-Like Oscillating Background: Scenarios of Long-Time Asymptotics	2021	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+ PDF Chat	Long-Time Asymptotics for the Integrable Nonlocal Focusing Nonlinear Schrödinger Equation for a Family of Step-Like Initial Data	2021	Yan Rybalko Dmitry Shepelsky
+	Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation	2021	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Defocusing Nonlocal Nonlinear Schrödinger Equation with Step-like Boundary Conditions: Long-time Behavior for Shifted Initial Data	2020	Yan Rybalko Dmitry Shepelsky
+	Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data	2020	Yan Rybalko Dmitry Shepelsky
+	The focusing NLS equation with step-like oscillating background: asymptotics in a transition zone	2020	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+ PDF Chat	A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions	2020	Anne Boutet de Monvel Iryna Karpenko Dmitry Shepelsky
+ PDF Chat	Nonlinear Fourier Spectrum Characterization of Time-Limited Signals	2020	Dmitry Shepelsky Anastasiia Vasylchenkova Jaroslaw E. Prilepsky Iryna Karpenko
+	The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem	2020	Anne Boutet de Monvel Iryna Karpenko Dmitry Shepelsky
+	The focusing NLS equation with step-like oscillating background: asymptotics in a transition zone	2020	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+	The focusing NLS equation with step-like oscillating background: the genus 3 sector	2020	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+	Long-time asymptotics for the integrable nonlocal focusing nonlinear Schr\"odinger equation for a family of step-like initial data	2019	Yan Rybalko Dmitry Shepelsky
+	On the rigorous justification of b-modulation method and inclusion of discrete eigenvalues	2019	Dmitry Shepelsky Anastasiia Vasylchenkova Jaroslaw E. Prilepsky Iryna Karpenko
+	Nonlinear Fourier spectrum characterization of time-limited signals	2019	Dmitry Shepelsky Anastasiia Vasylchenkova Jaroslaw E. Prilepsky Iryna Karpenko
+ PDF Chat	Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation	2019	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Long-time asymptotics for the Degasperis–Procesi equation on the half-line	2019	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+	Nonlinear Fourier spectrum characterization of time-limited signals	2019	Dmitry Shepelsky Anastasiia Vasylchenkova Jaroslaw E. Prilepsky Iryna Karpenko
+	Riemann-Hilbert approach for the integrable nonlocal nonlinear Schr\"odinger equation with step-like initial data	2018	Yan Rybalko Dmitry Shepelsky
+ PDF Chat	Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation	2018	Anastasiia Vasylchenkova Jaroslaw E. Prilepsky Dmitry Shepelsky Amit K. Chattopadhyay
+	Data underpinning article "Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrodinger equation"	2018	Anastasiia Vasylchenkova Yaroslav Prylepskiy Dmitry Shepelsky Amit K. Chattopadhyay
+ PDF Chat	The short pulse equation by a Riemann–Hilbert approach	2017	Anne Boutet de Monvel Dmitry Shepelsky Lech Zieliński
+	Planar unimodular Baker-Akhiezer function for the nonlinear Schrödinger equation	2017	Vladimir Kotlyarov Dmitry Shepelsky
+	The inverse scattering transform in the form of a Riemann-Hilbert problem for the Dullin-Gottwald-Holm equation	2016	Dmitry Shepelsky Lech Zieliński
+ PDF Chat	A Riemann-Hilbert Approach for the Novikov Equation	2016	Anne Boutet de Monvel Dmitry Shepelsky Lech Zieliński
+ PDF Chat	THE SHORT PULSE EQUATION BY A RIEMANN-HILBERT APPROACH	2016	Anne Boutet de Monvel Dmitry Shepelsky Lech Zieliński
+ PDF Chat	Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation	2015	Spyridon Kamvissis Dmitry Shepelsky Lech Zieliński
+	Long-time asymptotics for the Degasperis-Procesi equation on the half-line	2015	Anne Boutet de Monvel Jonatan Lenells Dmitry Shepelsky
+ PDF Chat	The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach	2014	Anne Boutet de Monvel Dmitry Shepelsky
+	Chapter 3: Evolution Problems: Nonlinear	2014	Gino Biondini A. S. Fokas Dmitry Shepelsky
+	Spectral Theory and Differential Equations	2014	E. Ya. Khruslov L. А. Pastur Dmitry Shepelsky
+ PDF Chat	The Ostrovsky–Vakhnenko equation: A Riemann–Hilbert approach	2014	Anne Boutet de Monvel Dmitry Shepelsky
+	On the spectrum of nonself-adjoint Zakharov–Shabat operators on R	2014	Thomas Kappeler Philipp Lohrmann Peter Topalov E. Ya. Khruslov L. А. Pastur Dmitry Shepelsky
+	Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation	2014	Spyridon Kamvissis Dmitry Shepelsky Lech Zieliński
+	The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach	2013	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	A Riemann–Hilbert approach for the Degasperis–Procesi equation	2013	Anne Boutet de Monvel Dmitry Shepelsky
+	The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach	2013	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	Initial boundary value problem for the focusing nonlinear Schrödinger equation with Robin boundary condition: half-line approach	2012	Alexander Its Dmitry Shepelsky
+	The short-wave model for the Camassa–Holm equation: a Riemann–Hilbert approach	2011	Anne Boutet de Monvel Dmitry Shepelsky Lech Zieliński
+	INVERSE SCATTERING TRANSFORM FOR THE DEGASPERIS-PROCESI EQUATION: A RIEMANN-HILBERT APPROACH	2011	Anne Boutet De Monveland Dmitry Shepelsky
+	A Riemann-Hilbert approach for the Degasperis-Procesi equation	2011	Anne Boutet de Monvel Dmitry Shepelsky
+	Initial-Boundary Value Problem for the Camassa–Holm Equation with Linearizable Boundary Condition	2010	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	Initial boundary value problems for integrable systems: towards the long time asymptotics	2010	Anne Boutet de Monvel Vladimir Kotlyarov Dmitry Shepelsky Chunxiong Zheng
+	Focusing NLS Equation: Long-Time Dynamics of Step-Like Initial Data	2010	Anne Boutet de Monvel Vladimir Kotlyarov Dmitry Shepelsky
+ PDF Chat	The Camassa–Holm equation on the half-line with linearizable boundary condition	2010	Anne Boutet de Monvel Dmitry Shepelsky
+	Painlevé-Type Asymptotics for the Camassa–Holm Equation	2010	Anne Boutet de Monvel Alexander Its Dmitry Shepelsky
+ PDF Chat	Long-time Asymptotics for the Camassa–Holm Equation	2009	Anne Boutet de Monvel Aleksey Kostenko Dmitry Shepelsky Gerald Teschl
+ PDF Chat	Long time asymptotics of the Camassa–Holm equation on the half-line	2009	Anne Boutet de Monvel Dmitry Shepelsky
+	Decaying Long-Time Asymptotics for the Focusing NLS Equation with Periodic Boundary Condition	2008	Anne Boutet de Monvel Vladimir Kotlyarov Dmitry Shepelsky
+	The Camassa–Holm Equation on the Half-Line: a Riemann–Hilbert Approach	2008	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	E.Ya.Khruslov. On the occasion of his 70th birthday	2008	V. V. Marchenko Klavdii V. Maslov Dmitry Shepelsky V. V. Zhikov
+	Riemann--Hilbert problem in the inverse scattering for the Camassa--Holm equation on the line	2008	Anne Boutet de Monvel Dmitry Shepelsky
+	THE FOCUSING NLS EQUATION WITH PERIODIC DIRICHLET DATA: ADMISSIBLE NEUMANN VALUES AND LONG-TIME ASYMPTOTICS	2008	Anne Boutet de Monvel Vladimir Kotlyarov Dmitry Shepelsky
+ PDF Chat	Long-time asymptotics of the Camassa-Holm equation on the line	2008	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	Riemann–Hilbert approach for the Camassa–Holm equation on the line	2006	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	Integrable Nonlinear Evolution Equations on a Finite Interval	2006	Anne Boutet de Monvel A. S. Fokas Dmitry Shepelsky
+ PDF Chat	Multiparameter reconstruction for a stratified coating on a reflecting support	2006	Dmitry Shepelsky V. N. Fenchenko
+	Riemann–Hilbert Methods in Integrable Systems	2006	Dmitry Shepelsky
+	Riemann–Hilbert Methods in Integrable Systems	2006	Dmitry Shepelsky
+ PDF Chat	The Camassa–Holm equation on the half-line	2005	Anne Boutet de Monvel Dmitry Shepelsky
+	THE mKdV EQUATION ON THE HALF-LINE	2004	Anne Boutet de Monvel A. S. Fokas Dmitry Shepelsky
+ PDF Chat	Initial boundary value problem for the mKdV equation on a finite interval	2004	Anne Boutet de Monvel Dmitry Shepelsky
+ PDF Chat	The modified KdV equation on a finite interval	2003	Anne Boutet de Monvel Dmitry Shepelsky
+	The mKdV equation on a finite interval	2003	Anne Boutet de Monvel Dmitry Shepelsky
+	Reconstruction of a stratified omega medium and the associated Riemann Hilbert problem	2002	Anne Boutet de Monvel Dmitry Shepelsky
+	A frequency–domain inverse problem for a dispersive stratified chiral medium	2000	Anne Boutet de Monvel Dmitry Shepelsky
+	Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium	2000	Dongwoo Sheen Dmitry Shepelsky
+	Inverse scattering problem for a stratified dispersive chiral medium	1999	Dmitry Shepelsky
+	Inverse scattering problem for a stratified anisotropic slab	1999	Dongwoo Sheen Dmitry Shepelsky
+	Inverse scattering problem for a stratified bi-isotropic medium at oblique incidence	1998	Anne Boutet de Monvel Dmitry Shepelsky
+	On the integrated density of states for a certain ensemble of random matrices	1998	Anne Boutet de Monvel Dmitry Shepelsky Mariya Shcherbina
+	Inverse scattering problem for anisotropic media	1995	Anne Boutet de Monvel Dmitry Shepelsky
+	The inverse problem of reconstruction of the medium’s conductivity in a class of discontinuous and increasing functions	1994	Dmitry Shepelsky
+	Inverse scattering method in electromagnetic sounding theory	1994	E. Ya. Khruslov Dmitry Shepelsky

Common Coauthors

Coauthor	Papers Together
Anne Boutet de Monvel	45
Yan Rybalko	15
Iryna Karpenko	10
Jaroslaw E. Prilepsky	9
Lech Zieliński	8
Jonatan Lenells	7
Anastasiia Vasylchenkova	7
Vladimir Kotlyarov	5
Stepan Bogdanov	4
E. Ya. Khruslov	3
A. S. Fokas	3
L. А. Pastur	2
Dongwoo Sheen	2
Alexander Its	2
Spyridon Kamvissis	2
Amit K. Chattopadhyay	2
Gerald Teschl	2
Ruslan Barkov	1
Yaroslav Prylepskiy	1
V. N. Fenchenko	1
V. V. Zhikov	1
Mariya Shcherbina	1
Thomas Kappeler	1
Gino Biondini	1
Peter Topalov	1
Anne Boutet De Monveland	1
Aleksey Kostenko	1
Philipp Lohrmann	1
Pedro J. Freire	1
Shou‐Fu Tian	1
Sergei K. Turitsyn	1
Egor Sedov	1
V. V. Marchenko	1
A Tiurdio	1
Klavdii V. Maslov	1
Chunxiong Zheng	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation	1993	Percy Deift Xin Zhou	35
+	Long-Time Asymptotics for Integrable Nonlinear Wave Equations	1993	Percy Deift A. R. Its Xin Zhou	20
+ PDF Chat	An integrable shallow water equation with peaked solitons	1993	Roberto Camassa Darryl D. Holm	19
+	The collisionless shock region for the long‐time behavior of solutions of the KdV equation	1994	Percy Deift Stephanos Venakides Xin Zhou	17
+	On the scattering problem for the Camassa-Holm equation	2001	Adrian Constantin	16
+ PDF Chat	A steepest descent method for oscillatory Riemann-Hilbert problems	1992	Percy Deift Xin Zhou	15
+ PDF Chat	Long-time Asymptotics for the Camassa–Holm Equation	2009	Anne Boutet de Monvel Aleksey Kostenko Dmitry Shepelsky Gerald Teschl	15
+	THE mKdV EQUATION ON THE HALF-LINE	2004	Anne Boutet de Monvel A. S. Fokas Dmitry Shepelsky	15
+	A unified transform method for solving linear and certain nonlinear PDEs	1997	A. S. Fokas	13
+ PDF Chat	Riemann–Hilbert approach for the Camassa–Holm equation on the line	2006	Anne Boutet de Monvel Dmitry Shepelsky	13
+	Scattering and inverse scattering for first order systems	1984	Richard Beals Ronald R. Coifman	13
+	The Riemann–Hilbert Problem and Inverse Scattering	1989	Xin Zhou	13
+ PDF Chat	The nonlinear Schrödinger equation on the half-line	2005	A. S. Fokas A. R. Its L-Y Sung	12
+ PDF Chat	Long‐time asymptotics of the nonlinear Schrödinger equation shock problem	2007	Robert Buckingham Stephanos Venakides	12
+ PDF Chat	Long-time asymptotics of the Camassa-Holm equation on the line	2008	Anne Boutet de Monvel Dmitry Shepelsky	12
+ PDF Chat	Long time asymptotics of the Camassa–Holm equation on the half-line	2009	Anne Boutet de Monvel Dmitry Shepelsky	12
+ PDF Chat	The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity	2017	Jonatan Lenells	12
+	None	2002	A. S. Fokas	11
+ PDF Chat	Inverse scattering transform for the Camassa–Holm equation	2006	Adrian Constantin Vladimir S. Gerdjikov Rossen I. Ivanov	10
+ PDF Chat	Initial boundary value problem for the mKdV equation on a finite interval	2004	Anne Boutet de Monvel Dmitry Shepelsky	10
+	None	1997	Percy Deift Stephanos Venakides Xiaowen Zhou	10
+	Painlevé-Type Asymptotics for the Camassa–Holm Equation	2010	Anne Boutet de Monvel Alexander Its Dmitry Shepelsky	10
+	Focusing NLS Equation: Long-Time Dynamics of Step-Like Initial Data	2010	Anne Boutet de Monvel Vladimir Kotlyarov Dmitry Shepelsky	9
+	Riemann--Hilbert problem in the inverse scattering for the Camassa--Holm equation on the line	2008	Anne Boutet de Monvel Dmitry Shepelsky	9
+ PDF Chat	Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability	2017	Gino Biondini Dionyssios Mantzavinos	8
+ PDF Chat	Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry	1998	Carl M. Bender Stefan Boettcher	8
+	Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions	2014	Gino Biondini Gregor Kovačič	8
+ PDF Chat	The Linearization of the Initial-Boundary Value Problem of the Nonlinear Schrödinger Equation	1996	A. S. Fokas A. R. Its	8
+ PDF Chat	The Scattering Approach for the Camassa—Holm equation	2002	Jonatan Lenells	7
+	Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach	2000	Percy Deift	7
+	Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data	2020	Yan Rybalko Dmitry Shepelsky	7
+	On solutions of the Camassa-Holm equation	2003	R. S. Johnson	7
+	The short-wave model for the Camassa–Holm equation: a Riemann–Hilbert approach	2011	Anne Boutet de Monvel Dmitry Shepelsky Lech Zieliński	7
+ PDF Chat	The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations	2008	Adrian Constantin David Lannes	7
+ PDF Chat	A Riemann–Hilbert approach for the Degasperis–Procesi equation	2013	Anne Boutet de Monvel Dmitry Shepelsky	7
+	The Camassa–Holm Equation on the Half-Line: a Riemann–Hilbert Approach	2008	Anne Boutet de Monvel Dmitry Shepelsky	7
+ PDF Chat	On the Inverse Scattering Approach to the Camassa-Holm Equation	2003	Adrian Constantin Jonatan Lenells	7
+ PDF Chat	The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach	2014	Anne Boutet de Monvel Dmitry Shepelsky	6
+	On the integrability of linear and nonlinear partial differential equations	2000	A. S. Fokas	6
+	Symplectic structures, their Bäcklund transformations and hereditary symmetries	1981	Benno Fuchssteiner A. S. Fokas	6
+	A Riemann-Hilbert approach for the Degasperis-Procesi equation	2011	Anne Boutet de Monvel Dmitry Shepelsky	6
+ PDF Chat	Regularization of a sharp shock by the defocusing nonlinear Schrödinger equation	2015	R. M. Jenkins	6
+ PDF Chat	Nonlinear waves in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">PT</mml:mi></mml:mrow></mml:math>-symmetric systems	2016	V. V. Konotop Jianke Yang Dmitry A. Zezyulin	6
+ PDF Chat	A new integrable equation with cuspons and W/M-shape-peaks solitons	2006	Zhijun Qiao	6
+ PDF Chat	Continuous and discrete Schrödinger systems with parity-time-symmetric nonlinearities	2014	Amarendra K. Sarma Mohammad‐Ali Miri Ziad H. Musslimani Demetrios N. Christodoulides	6
+ PDF Chat	Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation	2019	Yan Rybalko Dmitry Shepelsky	6
+	Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles	1986	Gerhard Kristensson Robert J. Krueger	5
+ PDF Chat	Parametric Representation for the Multisoliton Solution of the Camassa–Holm Equation	2005	Yoshimasa Matsuno	5
+ PDF Chat	Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions	2018	Mark J. Ablowitz Xu‐Dan Luo Ziad H. Musslimani	5
+ PDF Chat	Alice-Bob systems, P^-T^-Ĉ symmetry invariant and symmetry breaking soliton solutions	2018	Sen‐Yue Lou	5