Abstract 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. Painlevé II type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zero-order similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.
Received: 10 December 2008
Revised: 07 January 2009
Accepted manuscript online:
Fund: Project 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) and PCSIRT (Grant No IRT0734), the Research
Fund of Postdoctoral of China (Grant No 20070410727) and Specialized
Research Fund for the Doctoral Program of Higher Education of China
(Grant No 20070248120).
Cite this article:
Jiao Xiao-Yu(焦小玉) and Lou Sen-Yue(楼森岳) Approximate direct reduction method: infinite series reductions to the perturbed mKdV equation 2009 Chin. Phys. B 18 3611
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