Existence of periodic wave for a perturbed MEW equation

A perturbed MEW equation including small backward diffusion, dissipation and nonlinear term is considered by the geometric singular perturbation theory. Based on the monotonicity of the ratio of Abelian integrals, we prove the existence of periodic wave on a manifold for perturbed MEW equation. By Chebyshev system criterion, the uniqueness of the periodic wave is obtained. Furthermore, the monotonicity of the wave speed is proved and the range of the wave speed is obtained. Additionally, the monotonicity of period is given by Picard-Fuchs equation.