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 language | English |
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Pages (from-to) | 24-43 |
Number of pages | 20 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 121 |
Issue number | 1-2 |
DOIs | |
State | Published - 1998 |
Keywords
- Integrable PDEs
- Loop groups
- Solitons