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

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  • Borluk, H.
  • Muslu, G.M.
  • Erbay, H.A.

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-, 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.

Suggested Citation

  • Borluk, H. & Muslu, G.M. & Erbay, H.A., 2007. "A numerical study of the long wave–short wave interaction equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 113-125.
    • Handle: RePEc:eee:matcom:v:74:y:2007:i:2:p:113-125
    DOI: 10.1016/j.matcom.2006.10.016
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    1. Muslu, G.M. & Erbay, H.A., 2005. "Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(6), pages 581-595.
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