Persistence of kink and anti-kink wave solutions for the perturbed double sine-Gordon equation

Based on the geometric singular perturbation theory and the Melnikov method, we study the persistence of kink and anti-kink wave solutions for the perturbed double sine-Gordon equation. The explicit expression of the Melnikov function is given. Moreover, the monotonicity of the period function for unperturbed double sine-Gordon equation is investigated.(c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

Based on the geometric singular perturbation theory and the Melnikov method, this article studies the persistence of kink and anti-kink wave solutions in the perturbed double sine-Gordon equation. The explicit expression of the Melnikov function is provided. Furthermore, the monotonicity of the period function for the unperturbed double sine-Gordon equation is investigated.