| Abstract: |
| Wilton ripples are branches of traveling waves where the small amplitude solutions are composed of two co-propagating resonant harmonics. In this talk, we consider the simplest (1:2) resonant-triad configuration in a class of weakly nonlinear model equations. This class includes the Kawahara, Benjamin, Whitham, and Akers-Milewksi equations. Continuous branches of Wilton ripples are shown to exist via two independent proofs. Each proof technique has an associated numerical solution procedure. Both the proofs and numerical methods are compared. |
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