Wilton Ripples in Weakly Nonlinear Model Equations

Document Type

Article

Publication Date

2012

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.

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Reviewed at MR2911208

DOI

10.4310/CMS.2012.v10.n3.a15

Source Publication

Communications in Mathematical Sciences

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