Solitons from the Lagrangian perspective

Research output: Contribution to journalArticle

Abstract

The soliton solution of the Korteweg-de Vries equation provides a good approximation to the shape of a solitary wave solution to the governing equations for water waves. However, the corresponding velocity field below the soliton is not an accurate approximation. We propose an approach that provides us with a better approximation. By describing the particle paths below the free surface, we show that the qualitative features of the entire flow in a solitary water wave is captured by our approximation of the velocity field.

Details

Authors
  • Adrian Constantin
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • particle trajectory, solitary wave, soliton
Original languageEnglish
Pages (from-to)469-481
JournalDiscrete and Continuous Dynamical Systems. Series A
Volume19
Issue number3
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes