Search results for "Generalized Camassa-Holm Equations"

Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations

2014

In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do not support singular traveling waves. The third equation supports four-segmented, non-smooth $M$-wave solutions, while the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. Moreover, sm…