Interaction of solitons in a Boussinesq equation with dissipation

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Abstract

We investigate numerically an equation of Boussinesq type with square and cubic nonlinearity. In the model equation, dissipation is added and we investigate the physical properties of the modified problem. The technique applied here is the Christov spectral method in L 2(-∞, ∞). In previous works of the author, it was found that this technique was effective, accurate and computationally efficient for problems of this kind. Localized solutions are obtained numerically for the case of the moving frame which are used as initial conditions for the time-dependent problem. We investigate the propagation, head-on and overcome interaction of solitons. The issue of the phase shift is introduced and is been evaluated numerically.

Original languageEnglish
Pages (from-to)1397-1412
Number of pages16
JournalInternational Journal of Computer Mathematics
Volume90
Issue number7
DOIs
Publication statusPublished - Jul 2013

Keywords

  • dissipative solitons
  • solitons
  • spectral method

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