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Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method. (English) Zbl 1159.65348
Summary: 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.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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