Solitary waves of the generalized KdV equation with distributed delays

In this paper, we study an integro-differential equation based on the generalized KdV equation with a convolution term introduces a time delay in the nonlinearity. Special attention is paid to the existence of solitary wave solutions. Motivated [M.J. Ablowitz, H. Seger, Soliton and Inverse Scattering Transform, SIAM, Philadelphia, 1981; C.K.R.T. Jones, singular perturbation theory, in: R. Johnson (Ed.), Dynamical Systems, in: Lecture Notes in Math., vol. 1609, Springer, New 1995; T. Ogawa, Travelling wave solutions to perturbed Korteweg-de Vries equations, Hiroshima Math. J. 24 (1994) we prove, using the linear chain trick and geometric singular perturbation analysis, that the solitary wave solutions persist the average delay is suitably small, for a special convolution kernel. (C) 2008 Elsevier Inc. All rights reserved.