LAUSR

In this paper, we study a nonlinear fifth-order KdV equation which has wide physical applications. We first establish the existence of solitary wave solutions for this equation without delay by using the Hamilton function method. Then we obtain the desired homoclinic orbits by constructing a locally invariant manifold. Finally we obtain the existence of solitary wave solutions for this equation with local and nonlocal delay convolution kernels by using the geometric singular perturbation analysis, implicit function theorem and Fredholm theory.