A numerical study of the long wave-short wave interaction equations

Abstract

Two numerical methods are presented for the periodic initial-value problem of the long wave–short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the split-step Fourier method, which is of spectral-order accuracy in space. We consider the first-, secondand fourth-order versions of the split-step method, which are first-, secondand fourth-order accurate in time, respectively. The present split-step method profits from the existence of a simple analytical solution for the nonlinear subproblem. We numerically test both the relaxation method and the split-step schemes for a problem concerning the motion of a single solitary wave. We compare the accuracies of the split-step schemes with that of the relaxation method. Assessments of the efficiency of the schemes show that the fourth-order split-step Fourier scheme is the most efficient among the numerical schemes considered. © 2006 IMACS. Published by Elsevier B.V. All rights reserved.

DOI: 10.1016/j.matcom.2006.10.016

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Cite this paper

@article{Borluk2007ANS, title={A numerical study of the long wave-short wave interaction equations}, author={H. Borluk and Gulcin M. Muslu and H. A. Erbay}, journal={Mathematics and Computers in Simulation}, year={2007}, volume={74}, pages={113-125} }