This paper proves the existence of traveling wave solutions in Konopelchenko–Dubrovsky equation with Kuramoto–Sivashinsky perturbation. By a special transformation, we simplify the analysis of the traveling wave system. Geometric singular perturbation theory is applied to reduce the corresponding traveling wave equation to a regularly perturbed system on a locally invariant manifold. We provide conditions on the existence of periodic and solitary wave solutions. Poincaré and homoclinic bifurcation theories, together with Melnikov’s method, are employed to validate our results.
Wei et al. (Thu,) studied this question.