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The Influence of an External Force on a Solitary Wave

In: Differential Equations Theory, Numerics and Applications

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  • Roger Grimshaw

    (Monash University, Department of Mathematics)

Abstract

Using the forced Korteweg-de Vries equation as a generic model, we investigate the interaction of a solitary wave with an isolated external force of small amplitude, using both asymptotic analysis and numerical simulations. The analysis leads to a reduced dynamical system for the solitary wave amplitude and position, and this is analysed in detail. The theory predicts that the main regimes are passage, repulsion or trapping. These theoretical predictions are confirmed in our numerical simulations of the forced Korteweg-de Vries equation. Further, the effects of friction or variable force speed on these phenomoma will also be mentioned briefly.

Suggested Citation

  • Roger Grimshaw, 1997. "The Influence of an External Force on a Solitary Wave," Springer Books, in: E. van Groesen & E. Soewono (ed.), Differential Equations Theory, Numerics and Applications, pages 89-101, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5157-3_4
    DOI: 10.1007/978-94-011-5157-3_4
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