Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

Xiaoyu Jiao; Ruoxia Yao; S. Y. Lou

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

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arXiv · 0901.4593

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

Xiaoyu Jiao·Ruoxia Yao·S. Y. Lou

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Abstract

An approximate perturbed direct homotopy 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 solution 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 valid also for strong perturbations.

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Xiaoyu Jiao, Ruoxia Yao, S. Y. Lou. 2009-01-29. Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations. https://doi.org/10.1088/0256-307x%2F26%2F4%2F040202

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