The Camassa-Holm Equation: A Loop Group Approach

Details The Camassa-Holm Equation: A Loop Group Approach The Camassa-Holm Equation: A Loop Group Approach

1997-09-28

arxiv.org/abs/solv-int/9709010v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 7 figures; LaTeX with psfig

Scientific paper

10.1016/S0167-2789(98)00099-2

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 Backlund transformations of the equation. These are used to find 2-soliton solutions of the CH equation, as well as some novel singular solutions.

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