On the Similarity Solutions of the Calogero–Degasperis–Fokas Modified KdV Equation via Symmetry Method

Abstract

Using the symmetry method, we analyze the Calogero–Degasperis–Fokas modified KdV equation u_t+u_xxx−au_x³−f(u)u_x=0; a∈\\mathbbR, where the function f solves f'''(u)=8af′(u). The infinitesimals, similarity variables, dependent variables, and reduction to quadrature or exact solutions of this equation for physically realisable forms of f(u) are also obtained. Some interesting outcomes of this study are the deductions of the new exact solutions, that does not seem to have been reported in the literature.