Periodic Traveling Wave Solutions of a Singularly Perturbed Generalized mKdV Equation with Higher-Degree Nonlinearities

In this study, we investigate the existence of periodic traveling wave solutions for a singularly perturbed generalized mKdV (modified Korteweg–de Vries) equation with higher-degree nonlinearities. The presence of periodic traveling wave solutions is demonstrated by utilizing the monotonicity of the ratio of Abelian integrals. We also prove the monotonicity of the limit wave speed and further derive its upper and lower bounds. Finally, a numerical study is presented to illustrate the theoretical results.