Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
Abstract
A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa–Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.
DOI
https://doi.org/10.1007/s00332-019-09572-1
Recommended Citation
Ivanov, R., Lyons, T. & Orr, N. (2020). Camassa–Holm cuspons, solitons and their interactions via the dressing method. Journal of Nonlinear Sciences,30, pp. 225–260. doi:10.1007/s00332-019-09572-1
Included in
Mathematics Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons
Publication Details
Ivanov, R., Lyons, T. & Orr, N. Camassa–Holm Cuspons, Solitons and Their Interactions via the Dressing Method, J. Nonlinear Sci. 30 (2020) 225–260. https://doi.org/10.1007/s00332-019-09572-1