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This paper is concerned with decay and symmetry properties of solitary wavesolutions to a nonlocal shallow water wave model. It is shown that allsupercritical solitary wave solutions are symmetric and monotone on either sideof the crest. The proof is based on a priori decay estimates and the method ofmoving planes. Furthermore, a close relation between symmetric and travelingwave solutions is established.

Symmetry and decay of traveling wave solutions to the Whitham equation