Monotonicity of the periodic waves for the perturbed generalized defocusing mKdV equation

TL;DR

This paper investigates the monotonicity of periodic wave speeds in a perturbed generalized defocusing mKdV equation, extending previous results and confirming findings through numerical simulations.

Contribution

It extends the monotonicity analysis of wave speeds to the generalized case using geometric singular perturbation theory and Abelian integrals.

Findings

Limit wave speed c_0(h) is monotonic with respect to energy h.

A lower bound for the limit wave speed is established.

Numerical simulations verify theoretical results.

Abstract

In this paper, we study the existence of periodic waves for the perturbed generalized defocusing mKdV equation using the theory of geometric singular perturbation. By Abelian integral and involution operation, we prove that the limit wave speed c_0(h) is monotonic with respect to energy h,and the lower bound of the limit wave speed is found. These works extend the main result of Chen et al. (2018) to the generalized case. Some numerical simulations are conducted to verify the correctness of the theoretical analysis.