TY - JOUR
T1 - Camassa–Holm Cuspons, Solitons and Their Interactions via the Dressing Method
AU - Ivanov, Rossen
AU - Lyons, Tony
AU - Orr, Nigel
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85070229765&partnerID=8YFLogxK
U2 - 10.1007/s00332-019-09572-1
DO - 10.1007/s00332-019-09572-1
M3 - Article
AN - SCOPUS:85070229765
SN - 0938-8974
VL - 30
SP - 225
EP - 260
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
IS - 1
ER -