Author
Jalal Shatah
Other affiliations: New York University, Brown University
Bio: Jalal Shatah is an academic researcher from Courant Institute of Mathematical Sciences. The author has contributed to research in topics: Nonlinear system & Wave equation. The author has an hindex of 30, co-authored 66 publications receiving 6602 citations. Previous affiliations of Jalal Shatah include New York University & Brown University.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the effect of group invariance on the stability of solitary waves was studied and applications were given to bound states and traveling wave solutions of nonlinear wave equations, where the authors considered an abstract Hamiltonian system which is invariant under a group of operators.
1,557 citations
TL;DR: In this paper, a transformation is proposed to change Klein-Gordon's non-linearite cubique to a (3+1) dimension. But it is not a transformation that changes the solution of the original problem.
Abstract: On construit une transformation qui change l'equation a non-linearite cubique que l'on sait resoudre a (3+1) dimensions. On demontre que la solution du probleme original a le meme comportement asymptotique que l'equation de Klein-Gordon non lineaire
480 citations
Book•
01 Jan 1998TL;DR: The wave equation conservation laws Function spaces The linear wave equation wellposedness Semilinear wave equations Wave maps Wave maps with symmetry as discussed by the authors The wave equation Conservation laws and function spaces.
Abstract: The wave equation Conservation laws Function spaces The linear wave equation Well-posedness Semilinear wave equations Wave maps Wave maps with symmetry Notes Bibliography
461 citations
TL;DR: In this paper, the authors established a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation and the Schrodinger equation, where ε ≥ 0.
Abstract: We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u
tt−◃u+f(u)=0, and the nonlinear Schrodinger equation, −iu
t−◃u+f(u)=0.
386 citations
TL;DR: In this article, the existence of global solutions for the gravity water wave equation in dimension 3, in the case of small data, was proved by combining energy estimates which yield control of L 2 related norms with dispersive estimates, which give decay in L 8.
Abstract: We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L 8 . To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
358 citations
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08 Jun 2006
TL;DR: In this paper, the Korteweg de Vries equation was used for ground state construction in the context of semilinear dispersive equations and wave maps from harmonic analysis.
Abstract: Ordinary differential equations Constant coefficient linear dispersive equations Semilinear dispersive equations The Korteweg de Vries equation Energy-critical semilinear dispersive equations Wave maps Tools from harmonic analysis Construction of ground states Bibliography.
1,733 citations
TL;DR: In this article, the effect of group invariance on the stability of solitary waves was studied and applications were given to bound states and traveling wave solutions of nonlinear wave equations, where the authors considered an abstract Hamiltonian system which is invariant under a group of operators.
1,557 citations
TL;DR: In this paper, a nouvelle demonstration de la stabilite orbitale des solitons d'etat fondamental de l'equation de Schrodinger non lineaire is presented.
Abstract: On presente une nouvelle demonstration de la stabilite orbitale des solitons d'etat fondamental de l'equation de Schrodinger non lineaire pour une grande classe de non-linearites. On demontre la stabilite de l'onde solitaire pour l'equation de Korteweg-de Vries generalisee
932 citations
TL;DR: In this paper, the collapse of self-focusing waves described by the nonlinear Schrodinger (NLS) equation and the Zakharov equations in nonlinear optics and plasma turbulence is reviewed.
641 citations
TL;DR: In this paper, le comportement asymptotique des solutions de □u=0 ou □=∂ t 2 −∂ 1 2...−∂ n 2 pour des conditions initiales u=0, u t =g(x) en t=0.
Abstract: On etudie le comportement asymptotique des solutions de □u=0 ou □=∂ t 2 −∂ 1 2 ...−∂ n 2 pour des conditions initiales u=0, u t =g(x) en t=0, avec g reguliere a support compact dans R n
592 citations