Approximate Homotopy Direct Reduction Method: Infinite Series Reductions to Perturbed mKdV Equations

doi:10.1088/0256-307X/26/4/040202

Chin. Phys. Lett.

2009, Vol. 26

Issue (4): 040202 DOI: 10.1088/0256-307X/26/4/040202

GENERAL

Approximate Homotopy Direct Reduction Method: Infinite Series Reductions to Perturbed mKdV Equations

JIAO Xiao-Yu¹, YAO Ruo-Xia^1,2,3, LOU Sen-Yu ^1,2,4

¹Department of Physics, Shanghai Jiao Tong University, Shanghai 200030²Department of Physics, Ningbo University, Ningbo 315211³School of Computer Science, Shaanxi Normal University, Xi'an 710062⁴School of Mathematics, Fudan University, Shanghai 200433

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JIAO Xiao-Yu, YAO Ruo-Xia, LOU Sen-Yu 2009 Chin. Phys. Lett. 26 040202

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Abstract An approximate homotopy direct reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth-order dispersion and second-order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solutions but also for the Painlevé II waves and periodic waves expressed by Jacobi elliptic functions for both fourth-order dispersion and second-order dissipation. The method is also valid for strong perturbations.

Keywords: 02.30.Jr

Received: 29 January 2009 Published: 25 March 2009

PACS:

02.30.Jr

(Partial differential equations)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/26/4/040202 OR https://cpl.iphy.ac.cn/Y2009/V26/I4/040202

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