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Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method

Parkes, E.J. and Abbasbandy, S. (2009) Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method. Numerical Methods for Partial Differential Equations, 25 (2). pp. 401-408. ISSN 0749-159X

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Abstract

The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear solitary waves.