Resumen de Existence of Kink Waves and Periodic Waves for a Perturbed Defocusing mKdV Equation

Aiyong Chen, Lina Guo, Wentao Huang

• The existence of kink waves and periodic waves for a perturbed defocusing mKdV equation is established by using geometric singular perturbation theory. In addition, by analyzing the perturbation of the Hamiltonian vector field with an elliptic Hamiltonian of degree four, a two saddle cycle is exhibited. It is proven that the wave speed c0(h) is decreasing on h∈[-3/4,0] by analyzing the ratio of Abelian integrals and the limit of wave speed is given. Furthermore, the relationship between the wave speed and the wavelength of traveling waves is obtained.