Soliton solutions for the Korteweg-de Vries equation by homotopy analysis method
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This article solves the well-known Korteweg-de Vries equation by the homotopy analysis method, an analytical, totally explicit technique. By choosing a proper auxiliary parameter, the new series solution converges rapidly to the exact solution, with a simple way to adjust the convergence region. In addition, we show that a significant improvement of the convergence rate and region is achieved by applying homotopy-pad/'e approximants. The present method holds promise in providing soliton solutions for more complicated wave equations.
The A N Z I A M Journal
© 2008 Cambridge University Press. Please refer to the journal's website for access to the definitive, published version.
Numerical Solution of Differential and Integral Equations