复合 Burgers-KdV 脉冲行为：折射、反射与融合
斑图形成与孤子
2025-05-26 v1 数学物理
math.MP
可精确求解与可积系统
摘要
我们考虑Burgers 方程与KdV 方程之间的耦合PDE系统，以建模浅水中类似「沟渠」结构与波状脉冲之间的相互作用。present two derivations of the resulting Burgers-swept KdV system, based on Lie group symmetry and reduced variational principles. exact compound soliton solutions are obtained, and numerical simulations show that the Burgers and KdV momenta tend toward a balance at which the coupled system reduces to the integrable Gardner equation. The numerical simulations also reveal rich nonlinear solution behaviours that include refraction, reflection, and soliton fusion, before the balance is finally achieved.
引用
@article{arxiv.2505.17026,
title = {Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion},
author = {Darryl D. Holm and Ruiao Hu and Oliver D. Street and Hanchun Wang},
journal= {arXiv preprint arXiv:2505.17026},
year = {2025}
}
备注
17 pages, 17 figures