Interacting localized waves for the regularized long wave equation via a Galerkin spectral method

M. A. Christou, C. I. Christov

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We develop a Fourier-Galerkin spectral technique for computing the solutions of type of interacting localized waves. To this end, a special complete orthonormal system of functions in L2(-∞,∞) is used and a time-stepping algorithm implementing the spectral method is developed. The rate of convergence of the coefficients is shown to be exponential. We consider the regularized long wave equation (RLWE) which is not fully integrable. We demonstrate the stability of the algorithm and find numerically the threshold for the existence of such interactions. We also calculate the phase shifts of the interactions and compare them to the finite-difference solution.

Original languageEnglish
Pages (from-to)257-268
Number of pages12
JournalMathematics and Computers in Simulation
Volume69
Issue number3-4
DOIs
Publication statusPublished - 24 Jun 2005

Keywords

  • Galerkin spectral method
  • Localized waves
  • Regularized long wave equation

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