The Camassa-Holm equation: A loop group approach

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Abstract

A map is presented that associates with each element of a loop group a solution of an equation related by a simple change of coordinates to the Camassa-Holm (CH) equation. Certain simple automorphisms of the loop group give rise to Bäcklund transformations of the equation. These are used to find 2-soliton solutions of the CH equation, as well as some novel singular solutions.

Original languageEnglish
Pages (from-to)24-43
Number of pages20
JournalPhysica D: Nonlinear Phenomena
Volume121
Issue number1-2
DOIs
StatePublished - 1998

Keywords

  • Integrable PDEs
  • Loop groups
  • Solitons

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