Stability of travelling wave solutions to the Whitham equation

Whitham-eqnThe paper “Stability of traveling wave solutions to the Whitham equation“, co-authored by N. Sanford, K. Kodama, J. Carter, and H. Kalisch, has been published in Physics Letters A.  The Whitham equation, shown above, is a model for waves on shallow water.  It admits a family of periodic travelling waves.  It is proved in this paper that small amplitude solutions with sufficient period are stable, but all large-amplitude traveling-wave solutions are unstable. A link to the paper is here.

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