Some new methods and results in the theory of \((2+1)\)-dimensional integrable equations

DOI10.1007/BF01016132zbMath0850.35094MaRDI QIDQ1918813

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

Publication date: 21 July 1996

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

spectral dataJost solutionsKadomtsev-Petviashvili equationdressing

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (7)

Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential ⋮ Extended resolvent and inverse scattering with an application to KPI ⋮ Dressing of a two-dimensional nontrivial potential ⋮ Modeling rogue waves with the Kadomtsev-Petviashvili (KP) equation ⋮ Solution of the Cauchy problem for the Boiti-Leon-Pempinelli equation ⋮ An Ablowitz-Ladik system with a discrete potential. I: Extended resolvent ⋮ Towards an inverse scattering theory for two-dimensional nondecaying potentials

Cites Work

• Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation
• The dressing method and nonlocal Riemann-Hilbert problems
• On the evolution of packets of water waves
• New features of Backlund and Darboux transformations in 2 + 1 dimensions
• Resolvent approach for the nonstationary Schrodinger equation
• Solutions of the KPI equation with smooth initial data
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