alexa Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation


Journal of Generalized Lie Theory and Applications

Author(s): Benno Fuchssteiner

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The main subject of the paper is to give a survey and to present new methods on how integrability results (i.e. results for symmetry groups, inverse scattering formulations, action-angle transformations and the like) can be transferred from one equation to others in case the equations are NOT related by Bäcklund transformations. As a main example the so-called Camassa-Holm equation is chosen for which the relevant results are obtained by having a look on the Korteweg de vries (KdV) equation. The Camassa-Holm equation turns out to be a different-factorization equation of the KdV, it describes shallow water waves and reconciles the properties which were known for different orders of shallow water wave approximations.

This article was published in Physica D: Nonlinear Phenomena and referenced in Journal of Generalized Lie Theory and Applications

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