Persistence of Traveling Wave Solutions of the Perturbed Klein‐Gordon‐Zakharov Equations

ABSTRACT This paper is concerned with the persistence of solitary wave solutions and periodic wave solutions of the perturbed Klein‐Gordon‐Zakharov equations (KGZEs). Combining geometric singular perturbation (GSP) theory, Melnikov methods, invariant manifold theory, and bifurcation theory, we prove that solitary wave solutions and periodic solutions of the KGZEs still persist under small perturbation when the specific wave velocity is selected. Additionally, we prove that the periodic orbits lead to the emergence of a hyperbolic limit cycle near the original periodic orbit when perturbed, and that other periodic orbits in the small neighborhood of the original periodic orbit break apart and tend to approach this hyperbolic limit cycle.