Single peak solitary wave and compacton solutions of the generalized two-component Hunter–Saxton system

Abstract

Dynamical system theory is applied to the generalized two-component Hunter–Saxton system. Two singular straight lines are found in the associated topological vector field. The influence of parameters as well as the singular lines on the smoothness property of the traveling wave solutions is explored in detail. We obtain the single peak solitary wave and compacton solutions for the generalized two-component Hunter–Saxton system. Asymptotic analysis and numerical simulations are provided for smooth solitary wave, peakon, cuspon and compacton solutions of the generalized two-component Hunter–Saxton system.