Journal ArticleDOI
On the Cauchy problem for the Kadomstev-Petviashvili equation
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This article is published in Geometric and Functional Analysis.The article was published on 1993-07-01. It has received 180 citations till now. The article focuses on the topics: Cauchy problem & Cauchy's convergence test.read more
Citations
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Well-posedness and scattering for the KP-II equation in a critical space
TL;DR: In this paper, it was shown that for arbitrarily large initial data the Cauchy problem is locally well-posed in the homogeneous space H ˙ − 1 2, 0 (R 2 ) and in the inhomogeneous spaceH − 12, 0( R 2 ), respectively.
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Solitary waves of generalized Kadomtsev-Petviashvili equations
Anne de Bouard,Jean-Claude Saut +1 more
TL;DR: In this article, the existence and non-existence cases for localized solitary waves of generalized Kadomtsev-Petviashvili equations are classified according to the sign of the transverse dispersion coefficients and to the nonlinearity.
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Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
TL;DR: In this paper, the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces, is studied.
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Global well-posedness of the KP-I initial-value problem in the energy space
TL;DR: In this article, the KP-I initial value problem was shown to be NP-hard, and it was shown that the solution of the problem is polynomial in the number of vertices.
Journal ArticleDOI
Global well-posedness of the KP-I initial-value problem in the energy space
TL;DR: In this article, it was shown that the KP-I initial value problem is globally well-posed in the natural energy space of the equation, and that it can be solved efficiently.
References
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Journal ArticleDOI
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
Journal Article
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrodinger equations, II. The KdV-equation
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Degenerative dispersion laws, motion invariants and kinetic equations
TL;DR: In this paper, the average occupation numbers of the state with momentum k of a homogeneous nonlinear medium with dispersion law co(k) were introduced to describe the nonlinearity of the medium.
Journal ArticleDOI
On a new hierarchy of symmetries for the Kadomtsev-Petviashvili equation
H.H. Chen,Y. C. Lee,Jeng-Eng Lin +2 more
TL;DR: In this article, a hierarchy of symmetries for the Kadomtsev-Petviashvili equation is presented, which depend on the space and time variables explicitly.