The Camassa-Holm Equation: A Loop Group Approach
Jeremy Schiff
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.
Create a lesson
Related papers
Equations of Geodesic Deviation and the Inverse Scattering Transform
Vadim V. Varlamov
Polarization scattering by soliton-soliton collisions
V. S. Shchesnovich
On the bilinear equations for Fredholm determinants appearing in random matrices
J. Harnad
Airy Kernel and Painleve II
Craig A. Tracy, Harold Widom
p-adic Difference-Difference Lotka-Volterra Equation and Ultra-Discrete Limit
Shigeki Matsutani
On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies
Jen-Hsu Chang, Ming-Hsien Tu