Traveling Wave Solutions of Konopelchenko–Dubrovsky Equation with KS Perturbation

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.