Extended resolvent and inverse scattering with an application to KPI

DOI10.1063/1.1587874zbMath1062.37088OpenAlexW1965061174MaRDI QIDQ4833062

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

Publication date: 14 December 2004

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

Full work available at URL: https://doi.org/10.1063/1.1587874

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (9)

Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential ⋮ Spectral theory of the nonstationary Schrödinger equation with a two-dimensionally perturbed arbitrary one-dimensional potential ⋮ Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation ⋮ Commutator identities on associative algebras and the integrability of nonlinear revolution equations ⋮ Hirota difference equation and a commutator identity on an associative algebra ⋮ A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order ⋮ Lax pairs for higher-dimensional evolution PDEs and a 3+1 dimensional integrable generalization of the Burgers equation ⋮ Integrability, exact reductions and special solutions of the KP–Whitham equations ⋮ Hirota difference equation: inverse scattering transform, Darboux transformation, and solitons

Cites Work

• 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
• 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
• 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
• Solving the Kadomtsev - Petviashvili equation with initial data not vanishing at large distances

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