منابع مشابه
Derivation of the Zakharov equations
This paper continues the study, initiated in [28, 8], of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic e...
متن کاملInstabilities in Zakharov Equations
In [2], F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard’s type, implying that the Cauch...
متن کاملQuantum Zakharov Equations
In this paper we investigate the existence of soliton solutions for a modified form of the Zakharov equations describing modulational instabilities in quantum plasmas. In particular, we show that quantum effects suppress the easily identifiable soliton solutions, obtained in the adiabatic limit. In this limit, the quantum Zakharov equations become a coupled fourth order system, not amenable to ...
متن کاملNew Exact and Explicit Solutions of the Zakharov Equations and Generalized Zakharov Equations by the Quotient Trigonometric Function Expansion Method
In this work, by using a simple transformation technique, we have show that the nonlinear wave equations: Zakharov equations and generalized Zakharov equations can be reduced to the same family of Duffing or double-well Duffing equations. Then by means of quotient trigonometric function expansion method, many kinds of exact and explicit solutions of this family of equations are obtained in a un...
متن کاملSpace Propagation of Instabilities in Zakharov Equations
In this paper we study an initial boundary value problem for Zakharov’s equations, describing the space propagation of a laser beam entering in a plasma. We prove a strong instability result and prove that the mathematical problem is ill-posed in Sobolev spaces. We also show that it is well posed in spaces of analytic functions. Several consequences for the physical consistency of the model are...
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ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2006
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-006-0034-4