Concentration Compactness and the Stability of Solitary-Wave Solutions to Nonlocal Equations
نویسندگان
چکیده
In their proof of the stability of standing-wave solutions of nonlinear Schrödinger equations, Cazenave and Lions used the principle of concentration compactness to characterize the standing waves as solutions of a certain variational problem. In this article we first review the techniques introduced by Cazenave and Lions, and then discuss their application to solitary-wave solutions of nonlocal nonlinear wave equations. As an example of such an application, we include a new result on the stability of solitary-wave solutions of the Kubota-Ko-Dobbs equation for internal waves in a stratified fluid.
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