Wilton ripples in weakly nonlinear model equations

Abstract

Traveling near-bichromatic solutions supported at resonant frequencies are computed in a family of nonlinear model equations. Wilton's expansion is calculated for these solutions to all orders, and used as the basis for a perturbative numerical method for computing near-bichromatic traveling waves. The perturbative method relies on the analyticity of solutions with respect to wave amplitude. Results are compared to a non-perturbative continuation method, and a method for proving analyticity of solutions is proposed.