@article{Wei2026, 
author = {Minzhi Wei and Feiting Fan and Xinxin Liu},
title = {Dynamics on traveling wave solutions for Broer-Kaup equation with distributed delay},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {857-880},
keywords = {delayed Broer-Kaup equation, bifurcation theory, involution mapping criterion, Melnikov function, traveling wave solution},
url = {https://www.sciopen.com/article/10.3934/math.2026037},
doi = {10.3934/math.2026037},
abstract = {This paper investigates the traveling wave solutions of the Broer-Kaup equation with distributed delay. Using geometric singular perturbation theory and the Melnikov function method, a qualitative analysis on the traveling wave equation is carried out. By restricting the system to a locally invariant manifold, the delayed traveling wave equation is reduced to a near-Hamiltonian system. A translation transformation is applied to simplify the near-Hamiltonian planar system. Through involution mapping criterion, the monotonicity of the ratio of two Abelian integrals is established, which ensures that the Melnikov function possesses a unique simple zero. Based on Poincaré and heteroclinic bifurcation theory, the sufficient conditions on the persistence of periodic and kink (anti-kink) wave solutions are derived. Moreover, we present numeric simulations to illustrate the given results.}
}