Abstract:We consider the a priori regularity and symmetry of periodic traveling wave solutions to a class of weakly dispersive equations with cubic nonlinearity. We prove that any continuous periodic traveling wave solution of small amplitude is symmetric if it satisfies the reflection criterion proposed recently by Bruell and Pei. Moreover, we confirm that continuous periodic traveling waves with singular crests or troughs, which correspond to large‐amplitude waves, are also symmetric if some cancellation structure ap… Show more
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