On the cauchy problem for kadomtsev-petviashvili equation

DOI10.1080/03605309908821468zbMath0934.35161OpenAlexW1966061913MaRDI QIDQ4261547

Nickolay Tzvetkov

Publication date: 11 November 1999

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309908821468

zbMATH Keywords

Cauchy problemlocal well-posednessKadomtsev-Petviashvili equationBourgain method

Mathematics Subject Classification ID

Related Items (16)

The Cauchy Problem for the Kadomtsev-Petviashvili (KPII) Equation in Three Space Dimensions ⋮ Bilinear space-time estimates for linearised KP-type equations on the three-dimensional torus with applications ⋮ Gevrey regularity for the generalized Kadomtsev-Petviashvili I (gKP-I) equation ⋮ Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations ⋮ The Cauchy problem for the rotation-modified Kadomtsev-Petviashvili type equation ⋮ The Cauchy problem for a two-dimensional generalized Kadomtsev–Petviashvili-I equation in anisotropic Sobolev spaces ⋮ Global well-posedness for the fifth order Kadomtsev-Petviashvili II equation in three dimensional space ⋮ Well-posedness of the Kadomtsev-Petviashvili-II in the negative Sobolev space with respect to y direction ⋮ Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations ⋮ LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES ⋮ Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941] ⋮ Well-posedness and regularity of the fifth order Kadomtsev-Petviashvili I equation in the analytic Bourgain spaces ⋮ On the Propagation of Regularity of Solutions of the Kadomtsev--Petviashvili Equation ⋮ On the propagation of regularities in solutions of the fifth order Kadomtsev-Petviashvili II equation ⋮ Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces ⋮ Justification of the KP-II approximation in dynamics of two-dimensional FPU systems

Cites Work

• Inverse scattering for the heat operator and evolutions in \(2+1\) variables
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the Cauchy problem for the Zakharov system
• On the (generalized) Korteweg-de Vries equation
• Quadratic forms for the 1-D semilinear Schrödinger equation

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