Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation

Jundong WANG, Man Wai YUEN, Lijun ZHANG

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Abstract

The existence of solitary wave solutions for a perturbed generalized mKdV equation with a cubic evolution term is investigated. All possible solitary waves for the corresponding unperturbed equation are firstly explored by dynamical system analysis. Then by using geometric singular perturbation theory and Melnikov's method, we prove that two solitary wave solutions of the unperturbed generalized mKdV equation with particularly chosen wave speeds will persist under small singular perturbation. The results of numerical simulations are consistent with our theoretical analysis. Copyright © 2021 Elsevier Ltd. All rights reserved.
Original languageEnglish
Article number107668
JournalApplied Mathematics Letters
Volume124
Early online dateSep 2021
DOIs
Publication statusE-pub ahead of print - Sep 2021

Citation

Wang, J., Yuen, M., & Zhang, L. (2022). Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation. Applied Mathematics Letters, 124. Retrieved from https://doi.org/10.1016/j.aml.2021.107668

Keywords

  • The perturbed mKdV equation
  • Solitary wave solution
  • Geometric singular perturbation theory
  • Melnikov’s function

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