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

Borluk H., Muslu G. M. , ERBAY H. A.

MATHEMATICS AND COMPUTERS IN SIMULATION, vol.74, pp.113-125, 2007 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74
  • Publication Date: 2007
  • Doi Number: 10.1016/j.matcom.2006.10.016
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.113-125


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-, second- and fourth-order versions of the split-step method, which are first-, second- and 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. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.