Results 1 
9 of
9
Strong instability of standing waves for nonlinear KleinGordon equation and . . . system
, 2008
"... ..."
C.: Nonreasonant smoothing for coupled wave + transport equations and the VlasovMaxwell system
 Revista Mat. Iberoamericana
, 2004
"... ..."
(Show Context)
Semidiscretization in time for nonlinear Schrödingerwaves equations
"... : In this paper, we are concerned with CrankNicolson like schemes for: (NLW! ) 1 ! 2 @ 2 t E! \Gamma i@ t E! \Gamma \DeltaE ! = jE! j 2oe E! : We present two schemes for which we give some convergence results. On of the scheme is dissipative and we describe precisely the dissipation. We prov ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
: In this paper, we are concerned with CrankNicolson like schemes for: (NLW! ) 1 ! 2 @ 2 t E! \Gamma i@ t E! \Gamma \DeltaE ! = jE! j 2oe E! : We present two schemes for which we give some convergence results. On of the scheme is dissipative and we describe precisely the dissipation. We prove that the solution of the second scheme fits that of (NLW! ) while the first one compute a average value of the solution. Key words: Wave equation, Schrodinger Equation, CrankNicolson schemes, oscillations. 1 Introduction. 1.1 Setting of the problem. The aim of this paper is to discuss the behaviour of two schemes for the timeenvelope approximation in plasma physics studied in [3]. Let us first recall what is the timeenvelope approximation in plasma Physics. In a plasma medium, the electrostatic field E statisfies the following wave equation: @ 2 t E + ! 2 pe E \Gamma 3v 2 th \DeltaE = ! 2 pe " 0 N 0 T e jEj 2 E; where ! pe is the electronic plasma pulsation, v th is the...
From the KleinGordon Zakharov system to a singular nonlinear Schrödinger system
, 2008
"... In this paper, we continue our investigation of the highfrequency and subsonic limits of the KleinGordonZakharov system. Formally, the limit system is the nonlinear Schrödinger equation. However, for some special case of the parameters going to the limits, some new models arise. The main object o ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
In this paper, we continue our investigation of the highfrequency and subsonic limits of the KleinGordonZakharov system. Formally, the limit system is the nonlinear Schrödinger equation. However, for some special case of the parameters going to the limits, some new models arise. The main object of this paper is the derivation of those new models, together with convergence of the solutions along the limits. Résumé Du système de KleinGordon Zakharov vers un système de Schrödinger nonlinéaire sigulier. Dans cet article, on continue l’investigation des limites haute fréquence et subsonique du système de KleinGordonZakharov. Formellement, le système limite est le système de Schrödinger nonlinéaire. Cependant, pour un cas particulier des paramètres, on trouve un nouveau modèle qui contient un terme sigulier. L’objet de ce papier est de donner une dèrivation rigoureuse de ce moèle et de montrer la
Semidiscretization in time for Nonlinear Zakharov Waves Equations
 in "Discrete and Continuous Dynamical Systems: Series B
"... In this paper we construct and study discretizations of a nonlinear Zakharovwave system occurring in plasma physics. These systems are generalizations of the Zakharov system that can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular li ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
In this paper we construct and study discretizations of a nonlinear Zakharovwave system occurring in plasma physics. These systems are generalizations of the Zakharov system that can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular limit process. One of the scheme is conservative but sensible to the polarization of the initial data while the other one is able to handle illprepared initial data. We prove some convergence results and we perform some numerical tests.
TWO ASYMPTOTIC PROBLEMS FOR A SINGULAR NONLINEAR SCHRÖDINGER SYSTEM
"... Abstract. In this paper, we continue our investigation of the relation between various systems that can be derived from the KleinGordonZakharov system in the highfrequency and subsonic limits. In this paper we start from the singular nonlinear Schrödinger system which was derived in a previous wo ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we continue our investigation of the relation between various systems that can be derived from the KleinGordonZakharov system in the highfrequency and subsonic limits. In this paper we start from the singular nonlinear Schrödinger system which was derived in a previous work and derive the classical nonlinear Schrödinger system in two different limit cases. These two nonlinear Schrödinger systems have different coefficients in the nonlinearity.
Two asymptotic problems for a singular nonlinear Schrödinger system
, 2008
"... In this paper, we continue our investigation of the relation between various systems that can be derived from the KleinGordonZakharov system in the highfrequency and subsonic limits. In this paper we start from the singular nonlinear Schrödinger system which was derived in [15] and derive the cla ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we continue our investigation of the relation between various systems that can be derived from the KleinGordonZakharov system in the highfrequency and subsonic limits. In this paper we start from the singular nonlinear Schrödinger system which was derived in [15] and derive the classical nonlinear Schrödinger system in two different limit cases. These two nonlinear Schrödinger systems have different coefficients in the nonlinearity. 1
unknown title
, 2002
"... Consider a system consisting of a linear wave equation coupled to a transport equation: 2 t;x u = f; t + v() r ..."
Abstract
 Add to MetaCart
(Show Context)
Consider a system consisting of a linear wave equation coupled to a transport equation: 2 t;x u = f; t + v() r