Approximate similarity reduction for the perturbed mKdV equation via symmetry perturbation and direct method

作者:Liu, Xi zhong*
来源:Journal of Physics A-Mathematical and Theoretical, 2010, 43(26): 265203.
DOI:10.1088/1751-8113/43/26/265203

摘要

The perturbed mKdV equation with the general form is investigated in terms of the approximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions of different orders are obtained for both methods; series reduction solutions are consequently derived. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations. By comparison, the relation between the results obtained by applying the two methods is revealed.