Existence and stability of traveling waves for semi-relativistic Schrödinger equations with van der Waals-type potentials

Abstract

In this paper, we prove the existence and stability of traveling waves for semi-relativistic Schrödinger equations with van der Waals-type potentials. Using the concentration-compactness principle, we study the corresponding constraint minimization problem of equations and obtain the existence of traveling waves with subcritical arbitrarily small mass. Moreover, we show that the set of boosted ground states is a stable set. Our results contribute to the study of traveling wave solutions and the dynamics of semi-relativistic Schrödinger equations with van der Waals-type potentials.