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

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

2009-01-29

arxiv.org/abs/0901.4593v1

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, 1 figure

Scientific paper

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

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 Painlev\'e 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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