Inverse scattering theory of the heat equation for a perturbed one-soliton potential

DOI10.1063/1.1427410zbMath1059.35112OpenAlexW2090238060MaRDI QIDQ4830724

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

Publication date: 14 December 2004

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

Full work available at URL: https://semanticscholar.org/paper/cd1d7c6db361ab8076f5cf24fccf2bc6770150a1

Mathematics Subject Classification ID

Related Items (14)

Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential ⋮ The Riemann-Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient \((2+1)\)-dimensional KdV equation ⋮ Extended resolvent of the heat operator with a multisoliton potential ⋮ Weakly decaying solutions of nonlinear Schrödinger equation in the plane ⋮ The direct scattering problem for the perturbed Gr(1, 2) _⩾0 Kadomtsev–Petviash-vili II solitons ⋮ The direct scattering problem for perturbed Kadomtsev–Petviashvili multi line solitons ⋮ Discrete spectrum of \(2 + 1\)-dimensional nonlinear Schrödinger equation and dynamics of lumps ⋮ Whitham modulation theory for the Kadomtsev– Petviashvili equation ⋮ On critical behaviour in generalized Kadomtsev-Petviashvili equations ⋮ The equivalence of different approaches for generating multisoliton solutions of the KPII equation ⋮ Kadomtsev-Petviashvili Equation Revisited and Integrability in 4 + 2 and 3 + 1 ⋮ Dynamics of Lump Solutions in a 2 + 1 NLS Equation ⋮ Building an extended resolvent of the heat operator via twisting transformations ⋮ Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions

Cites Work

• Dressing of a two-dimensional nontrivial potential
• Inverse scattering for the heat operator and evolutions in \(2+1\) variables
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Towards an inverse scattering theory for non-decaying potentials of the heat equation
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• Resolvent approach for the nonstationary Schrodinger equation
• Properties of solutions of the Kadomtsev–Petviashvili I equation
• Solving the Kadomtsev - Petviashvili equation with initial data not vanishing at large distances
• Inverse scattering transform for the perturbed 1-soliton potential of the heat equation

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