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The Camassa-Holm Equation: A Loop Group Approach

Jeremy Schiff
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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 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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Jeremy Schiff. 1997-09-28. The Camassa-Holm Equation: A Loop Group Approach. https://doi.org/10.1016/s0167-2789(98)00099-2

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