EXISTENCE OF TRAVELING WAVES FOR A CLASS OF NONLOCAL NONLINEAR EQUATIONS WITH BELL SHAPED KERNELS

In this article we are concerned with the existence of traveling wave solutions of a general class of nonlocal wave equations: u(tt) - a(2) u(xx) (beta* u(p))(xx) p > 1. Members of the class arise as mathematical models for the propagation of waves in a wide variety of situations. We assume that the kernel beta is a bell-shaped function satisfying some mild differentiability and growth conditions. Taking advantage of growth properties of bell-shaped functions, we give a simple proof for the existence of bell-shaped traveling wave solutions.