内容介绍：In this talk, we first introduce the latest progresses and existing problems of traveling wave solutions in a class of perturbed generalized KdV equations. Then, for some general cases, we prove the persistence of periodic wave solutions with certain wave speeds under small perturbation by using geometric singular perturbation theory and analyzing the perturbations of a Hamiltonian system with two arbitrarily high-order terms. In addition, some properties of traveling wave solutions are obtained. Our results include and generalize known results. Moreover, our proofs are much simpler and shorter than existing ones. The talk includes joint works with Minzhi Wei, Yangjian Sun, Maoan Han and Changjian Liu.