Soliton evolution and radiation loss for the Korteweg-de Vries equation

William L Kath*, N. F. Smyth

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The time-dependent behavior of solutions of the Korteweg-de Vries (KdV) equation for nonsoliton initial conditions is considered. While the exact solution of the KdV equation can in principle be obtained using the inverse scattering transform, in practice it can be extremely difficult to obtain information about a solution's transient evolution by this method. As an alternative, we present here an approximate method for investigating this transient evolution which is based upon the conservation laws associated with the KdV equation. Initial conditions which form one or two solitons are considered, and the resulting approximate evolution is found to be in good agreement with the numerical solution of the KdV equation. Justification for the approximations employed is also given by way of the linearized inverse scattering solution of the KdV equation. In addition, the final soliton state determined from the approximate equations agrees very well with the final state determined from the exact inverse scattering transform solution.

Original languageEnglish (US)
Pages (from-to)661-670
Number of pages10
JournalPhysical Review E
Issue number1
StatePublished - Jan 1 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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