Traveling Wave Solutions to the Three-dimensional Nonlinear Viscoelastic System

Abstract

In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial traveling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.