Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 59, Issue 2, Pages 117-131Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1014933316169
Keywords
Camassa-Holm equation; pseudo-spherical surfaces; geometric integrability; Miura transformation; conservation law; nonlocal symmetry
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It is observed that the Camassa-Holm equation describes pseudo-spherical surfaces and that therefore, its integrability properties can be studied by geometrical means. An sl(2, R)-valued linear problem whose integrability condition is the Camassa-Holm equation is presented, a 'Miura transform' and a 'modified Camassa-Holm equation' are introduced, and conservation laws for the Camassa-Holm equation are then directly constructed. Finally, it is pointed out that this equation possesses a nonlocal symmetry, and its flow is explicitly computed.
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