The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal cohere...The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.展开更多
基金supported by the National Natural Science Foundations of China (Grant Nos 10735030,10475055,10675065 and 90503006)National Basic Research Program of China (Grant No 2007CB814800)+2 种基金PCSIRT (Grant No IRT0734)the Research Fund of Postdoctoral of China (Grant No 20070410727)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070248120)
文摘The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.
