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Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed \(N\)-soliton potential. (English) Zbl 1112.37068
Summary: In the framework of the extended resolvent approach, the direct and inverse scattering problems for the nonstationary Schrödinger equation with a potential being a perturbation of the \(N\)-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing \(N\) wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

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