Finding the One-Loop Soliton Solution of the Short-Pulse Equation by Means of the Homotopy Analysis Method

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.

short-pulse equation; homotopy analysis method; solitary-wave solution; series solution