3 research outputs found
Camassa-Holm cuspons, solitons and their interactions via the dressing method
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 ar re-examined in terms of quantities which can be explicitly
constructed via the inverse scattering method.Comment: 35 pages, 10 figures. arXiv admin note: text overlap with
arXiv:1702.0112
Integrable negative flows of the Heisenberg ferromagnet equation hierarchy
We study the negative flows of the hierarchy of the integrable Heisenberg ferromagnet model and their soliton solutions. The first negative flow is related to the so-called short pulse equation. We provide a framework which generates Lax pairs for the other members of the hierarchy. The application of the dressing method is illustrated with the derivation of the one-soliton solution