Numerical simulation of a generalized Zakharov system

  • Authors:

  • Shi Jin;Peter A. Markowich;Chunxiong Zheng

  • Affiliations:

  • Department of Mathematics, University of Wisconsin, Madison, WI and Department of Mathematical Science, Tsinghua University, Beijing 100084, PR China;Department of Mathematics, University of Vienna, Nordbergstrasse 15, A-1000 Vienna, Austria;Department of Mathematical Science, Tsinghua University, Beijing 100084, PR China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

In this paper, we propose and study two time-splitting spectral methods for the generalized Zakharov system. These methods are spectrally accurate in space, second order in time, and unconditionally stable. The unconditional stability of the methods offers greater numerical efficiency than those given in previous papers, especially in the subsonic regime. Our numerical experiments confirm the accuracy and stability. In particular, we analyze their behavior in the subsonic regime. The first method, using the exact time integration in phase space for the wave equation for the nondispersive field, converges unformly with respect to the sound speed for the dispersive wave field, while the second method, using the Crank-Nicolson method in the same step, with an initial layer fix by an L-stable time discretization, converges uniformly with respect to the sound speed for both dispersive and nondispersive fields. Using these new methods we also study the collision behavior of two solitons, in the subsonic region as well as the transsonic region. We obtain numerical results which are quantitatively different from those reported in previous papers using lower resolution numerical techniques.