Peakon, loop and solitary travelling wave solutions for the general modified CH–DP equation

Abstract: Travelling wave solutions for the general modified CH–DP equation u t − u xxt + αu 2 u x − βu x u xx = uu xxx are developed. By using the dynamical system method, a peakon and a dark soliton are found to coexist for the same wave speed. Exact explicit blow-up solutions are given. By using numerical simulation, a loop solution for a special case is discussed. [ABSTRACT FROM AUTHOR]