中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3611-3615.doi: 10.1088/1674-1056/18/9/001

• •    下一篇

Approximate direct reduction method: infinite series reductions to the perturbed mKdV equation

焦小玉1, 楼森岳2   

  1. (1)Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China; (2)Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China;Department of Physics, Ningbo University, Ningbo 315211, China
  • 收稿日期:2008-12-10 修回日期:2009-01-07 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:
    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).

Approximate direct reduction method: infinite series reductions to the perturbed mKdV equation

Jiao Xiao-Yu(焦小玉)a)† and Lou Sen-Yue(楼森岳)a)b)   

  1. a Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China; b Department of Physics, Ningbo University, Ningbo 315211, China
  • Received:2008-12-10 Revised:2009-01-07 Online:2009-09-20 Published:2009-09-20
  • Supported by:
    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).

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摘要： 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.

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.

Key words: perturbed mKdV equation, approximate direct reduction method, series reduction solutions

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Hq (Ordinary differential equations) 02.30.Jr (Partial differential equations)