Letters in Mathematical Physics

, Volume 59, Issue 2, pp 117–131

Geometric Integrability of the Camassa–Holm Equation

  • Enrique G. Reyes

DOI: 10.1023/A:1014933316169

Cite this article as:
Reyes, E.G. Letters in Mathematical Physics (2002) 59: 117. doi:10.1023/A:1014933316169


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.

Camassa–Holm equation pseudo-spherical surfaces geometric integrability Miura transformation conservation law nonlocal symmetry 

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Enrique G. Reyes
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenU.S.A.

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