Existence of periodic wave for a perturbed MEW equation

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 C...

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Bibliographic Details
Published in:AIMS mathematics Vol. 8; no. 5; pp. 11557 - 11571
Main Authors: Wei, Minzhi, He, Liping
Format: Journal Article
Language:English
Published: AIMS Press 01-01-2023
Subjects:
abelian integral
chebyshev system
geometric singular perturbation theory
periodic wave
perturbed mew equation
picard-fuchs equation
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023585