279 citations
- National Academy of Sciences of UkraineUA174 papers
- V. N. Karazin Kharkiv National UniversityUA37 papers
- Polish Academy of SciencesPL20 papers
- Leibniz Institute for Solid State and Materials ResearchDE12 papers
- University of GothenburgSE12 papers
- RIKENJP10 papers
- University of MichiganUS10 papers
- Chalmers University of TechnologySE9 papers
- Institute of PhysicsPL9 papers
- Centre National de la Recherche ScientifiqueFR8 papers
- Leibniz Institute of Photonic TechnologyDE8 papers
- University of Maryland, College ParkUS8 papers
6 papers · 1 filter
Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems
Dmitry Shepelsky, Iryna Karpenko, Stepan Bogdanov +1
We consider the Riemann--Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the sol…
The short pulse equation by a Riemann-Hilbert approach
Anne Boutet de Monvel, Dmitry Shepelsky, Lech Zielinski
We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation with zero boundary conditions (a…
Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation
Spyridon Kamvissis, Dmitry Shepelsky, Lech Zielinski
We consider the initial boundary value (IBV) problem for the focusing nonlinear Schrödinger equation in the quarter plane in the case of periodic initial data (at )…
Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds
Iryna Egorova, Johanna Michor, Gerald Teschl
We provide a rigorous treatment of the inverse scattering transform for the entire Toda hierarchy for solutions which are asymptotically close to (in general) different finite-gap…
Long-Time Asymptotics for the Camassa-Holm Equation
Anne Boutet de Monvel, Aleksey Kostenko, Dmitry Shepelsky +1
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa-Holm equation for decaying initial data, completing previous results by A. Bou…
On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations
Iryna Egorova, Katrin Grunert, Gerald Teschl
We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption…