aDepartment of Mathematics, University of Strathclyde, Livingstone Tower, Richmond Street, Glasgow G1 1XH, UK
bInstitute of Geophysics, Ukrainian Academy of Sciences, 03680 Kyiv, Ukraine
Abstract:
Explicit travelling-wave solutions of the Camassa–Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis–Procesi equation are given in an appendix.