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March  2009, 11(2): 263-282. doi: 10.3934/dcdsb.2009.11.263

Semi-discretization in time for nonlinear Zakharov waves equations

T. Colin 1, , Géraldine Ebrard 2, and  Gérard Gallice 2,

1. 

MAB, Université Bordeaux I and CNRS UMR 5466, 351 Cours de la Libération, 33405 Talence Cedex
2. 

CEA CESTA, SIS, BP 2, 33114 Le Barp, France, France

Received  November 2007 Revised  May 2008 Published  December 2008

In this paper we construct and study discretizations of an extension of the Zakharov system occurring in plasma physics. This system is intermediate between Euler-Maxwell and Zakharov systems. The usual Zakharov system can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular limit process and that are asymptotic preserving. We prove some stability and convergence results and we perform some numerical tests showing that the range of validity of the extended system is wider than that of the usual Zakharov system.
Keywords: Crank-Nicolson, Langmuir turbulence, Zakharov systems.
Mathematics Subject Classification: Primary: 65M06, 65M12, 78A60.
Citation: T. Colin, Géraldine Ebrard, Gérard Gallice. Semi-discretization in time for nonlinear Zakharov waves equations. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 263-282. doi: 10.3934/dcdsb.2009.11.263
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