Approximate homotopy symmetry and infinite series solutions to the perturbed mKdV equation

摘要

We devise a homotopy model for the perturbed mKdV equation with weak fourth order dispersion and weak dissipation, and demonstrate that the related approximate equations lead to similarity reduction equations and similarity reduction solutions of different orders which are formally coincident, respectively. Series reduction solutions for the perturbed mKdV equation are thus derived. Painlevé II type equations or hyperbolic secant function solutions are obtained for zero-order similarity reduction equations. Higher order similarity reduction equations are linear variable coefficients ordinary differential equations.