Bäcklund transformations for the Camassa-Holm equation
arXiv:1508.05636 · doi:10.1007/s00332-016-9325-6
Abstract
The Bäcklund transformation (BT) for the Camassa-Holm (CH) equation is presented and discussed. Unlike the vast majority of BTs studied in the past, for CH the transformation acts on both the dependent and (one of) the independent variables. Superposition principles are given for the action of double BTs on the variables of the CH and the potential CH equations. Applications of the BT and its superposition principles are presented, specifically the construction of travelling wave solutions, a new method to construct multi-soliton, multi-cuspon and soliton-cuspon solutions, and a derivation of generating functions for the local symmetries and conservation laws of the CH hierarchy.
References in corpus (3)
Cited by in corpus (7)
- Bäcklund Transformations for the Boussinesq Equation and Merging Solitons
- Camassa-Holm cuspons, solitons and their interactions via the dressing method
- A dressing method for soliton solutions of the Camassa-Holm equation
- Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis-Procesi Equation
- Computation of generating symmetries
- Nonlocal pseudosymmetries and Bäcklund transformations as -morphisms
- Symmetry structure of integrable hyperbolic third order equations