On finite energy solutions of the KP-I equation

DOI10.1007/s00209-007-0156-xzbMath1387.35530arXivmath/0603746OpenAlexW2087708426MaRDI QIDQ2463374

Herbert Koch, Nickolay Tzvetkov

Publication date: 6 December 2007

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603746

zbMATH Keywords

nonlinear wavesdispersive equationsKadomtsev-Petviashvili-I equation

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)

Related Items (15)

Global well-posedness of partially periodic KP-I equation in the energy space and application ⋮ A Geometric Proof of the Quasi-Linearity of the Water Waves System ⋮ Remark on the semilinear ill-posedness for a periodic higher-order KP-I equation ⋮ The Cauchy Problem for the Fractional Kadomtsev--Petviashvili Equations ⋮ Propagation of regularity and persistence of decay for fifth order dispersive models ⋮ Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations ⋮ Global solutions and stability properties of the 5th order Gardner equation ⋮ On the periodic Zakharov-Kuznetsov equation ⋮ Low regularity well-posedness for KP-I equations: the dispersion-generalized case ⋮ Well-posedness of the fifth order Kadomtsev-Petviashvili I equation in anisotropic Sobolev spaces with nonnegative indices ⋮ On the fifth-order KdV equation: Local well-posedness and lack of uniform continuity of the solution map ⋮ Recent Progress on the Global Well-Posedness of the KPI Equation ⋮ On the low regularity of the fifth order Kadomtsev-Petviashvili I equation ⋮ IST Versus PDE: A Comparative Study ⋮ Transverse nonlinear instability for two-dimensional dispersive models

Cites Work

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• Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
• On the local and global well-posedness theory for the KP-I equation
• Global well-posedness for the KP-I equation
• On equations of KP-type
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H¹(R)

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