Dynamics of Travelling Waves to KdV–Burgers–Kuramoto Equation with Marangoni Effect Perturbation.

This paper aims to establish the existence of travelling waves for a generalized KdV–Burgers–Kuramoto equation via utilising geometric singular perturbation theory. Firstly, we explore the existence results of orbits for the equation without delay and perturbation by employing Argument Principle. Secondly, the existence of travelling waves for the equation with two types of special delay convolution kernels are proved with the aid of combining the geometric singular perturbation theory, invariant manifold theory and Fredholm orthogonality theorem. Finally, asymptotic behaviors of traveling waves are given with the method of the asymptotic theory. [ABSTRACT FROM AUTHOR]