Compacton-Like Solutions in a Camassa–Holm Type Equation**Supported by the National Natural Science Foundation of China under Grant Nos. 11401274, 11271171 and Science and technology landing project of colleges and universities in Jiangxi Province under Grant Nos. KJLD14092, KJLD13093

Abstract

This paper shows that a Camassa–Holm type equation can be reduced to Hamiltonian system by transformation of variables. The hamiltonian system is studied by making use of the dynamical systems theory and the qualitative behavior of degenerate singular points is presented. In particular, new type of compacton-like solutions is obtained by setting the partial differential equation under boundary condition .