Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential

DOI10.1063/1.2393144zbMath1112.37068OpenAlexW2046192498MaRDI QIDQ3442144

M. Boiti, A. K. Pogrebkov, F. Pempinelli

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2393144

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Soliton equations (35Q51) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Quantum scattering theory (81Uxx)

Related Items (4)

Extended resolvent of the heat operator with a multisoliton potential ⋮ Whitham modulation theory for the Kadomtsev– Petviashvili equation ⋮ The equivalence of different approaches for generating multisoliton solutions of the KPII equation ⋮ Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions

Cites Work

• Spectral theory of the nonstationary Schrödinger equation with a two-dimensionally perturbed arbitrary one-dimensional potential
• Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation
• Towards an inverse scattering theory for two-dimensional nondecaying potentials
• Some new methods and results in the theory of \((2+1)\)-dimensional integrable equations
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• On the extended resolvent of the nonstationary Schrödinger operator for a Darboux transformed potential
• Resolvent approach for the nonstationary Schrodinger equation
• The Cauchy problem for the Kadomtsev–Petviashvili–I equation without the zero mass constraint
• Solutions of the KPI equation with smooth initial data
• Properties of solutions of the Kadomtsev–Petviashvili I equation
• Inverse scattering transform for the KPI equation on the background of a one-line soliton*
• Inverse scattering theory of the heat equation for a perturbed one-soliton potential
• Extended resolvent and inverse scattering with an application to KPI

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