Symmetry and decay of traveling wave solutions to the Whitham equation
arXiv:1608.07944 · doi:10.1016/j.jde.2017.01.011
Abstract
This paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model. It is shown that all supercritical solitary wave solutions are symmetric and monotone on either side of the crest. The proof is based on a priori decay estimates and the method of moving planes. Furthermore, a close relation between symmetric and traveling wave solutions is established.