Recent results on the generalized Kadomtsev-Petviashvili equations

DOI10.1007/BF00994650zbMath0839.35121OpenAlexW4255313102MaRDI QIDQ1896413

Jean Claude Saut

Publication date: 25 June 1996

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00994650

zbMATH Keywords

existenceinverse scattering transformuniquenessblowupreviewstability of solitonsglobal well-posedness of the Cauchy problem

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) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items

Strong instability of solitary-wave solutions to a Kadomtsev-Petviashvili equation in three dimensions, Solitary waves of generalized Kadomtsev-Petviashvili equations, Traveling wave solutions of a generalized modified Kadomtsev–Petviashvili equation, Extended shallow water wave equations, Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations, Existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation, Some generalizations of the Kadomtsev-Petviashvili equations, Solutions of the Generalized Rotation-Modified Kadomtsev-Petviashvili Equation, Soliton deflexion for \((1 + 3)\)D Kadomtsev-Petviashvili equation, Solitary waves for a class of generalized Kadomtsev-Petviashvili equation in \(\mathbb{R}^N\) with positive and zero mass, On the asymptotic behavior of solutions to the (generalized) Kadomtsev-Petviashvili-Burgers equations, Nondegeneracy, Morse index and orbital stability of the KP-I lump solution, Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation, The Cauchy problem and stability of solitary-wave solutions for RLW--KP-type equations

Cites Work

• Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Inverse scattering for the heat operator and evolutions in \(2+1\) variables
• Periodic solutions of Kadomtsev-Petviashvili
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation
• Solitary waves of generalized Kadomtsev-Petviashvili equations
• On multipliers of Fourier integrals in the spaces \(L_{p,\theta}\)
• The Cauchy problem for the Kadomtsev-Petviashvili equation
• Fully discrete galerkin methods for the korteweg-de vries equation
• On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Stability of Nonlinear Periodic Internal Waves in a Deep Stratified Fluid
• Properties of solutions of the Kadomtsev–Petviashvili I equation
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