Symmetry and decay of traveling wave solutions to the Whitham equation
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Original versionJournal of Differential Equations. 2017, 262 (8), 4232-4254. 10.1016/j.jde.2017.01.011
This paper is concerned with decay and symmetry properties of solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is shown that all such solitary-wave solutions are symmetric and monotone on either side of the crest. The proof is based on the method of moving planes. Furthermore, a close relation between symmetric and traveling-wave solutions is established.