发表机构
Universidade Estadual de Montes Claros; University of Southern Queensland（蒙特克里斯塔利斯州立大学; 昆士兰南部大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨Gardner-Ostrovsky方程中孤子的形成与相互作用，发现零总质量孤子可从脉冲扰动涌现，且相互作用非弹性，最终在封闭系统中仅最大振幅孤子存活，但孤子仍具鲁棒性。
AI 中文摘要
我们研究了具有反常（正）色散的非可积Gardner-Ostrovsky方程（又称旋转修正Gardner方程）中的孤子形成与相互作用。该方程与等离子体及其他色散介质中波动力学的描述相关。我们表明，一类具有零总质量和非单调渐近特性的特殊孤子可以从脉冲状初始扰动中涌现。根据初始条件的不同，这些孤子可能形成规则的振幅有序序列、不规则的相互作用局域结构非定态系综，或静止传播的多孤子复合体。我们进一步证明，Gardner-Ostrovsky方程中的孤子相互作用本质上是非弹性的，导致在封闭系统中出现占优的“孤子冠军”。例如，在周期性边界条件下，只有最大振幅的孤子最终存活，而所有较小的孤子通过连续相互作用逐渐被消除。尽管存在非弹性相互作用，Gardner-Ostrovsky孤子表现出显著的鲁棒性。
英文摘要
We investigate soliton formation and interactions in the non-integrable Gardner-Ostrovsky equation (alias the rotation-modified Gardner equation) with anomalous (positive) dispersion. This equation is relevant to the description of wave dynamics in plasmas and other dispersive media. We show that a special class of solitons, characterized by zero total mass and non-monotonic asymptotics, can emerge from pulse-like initial perturbations. Depending on the initial conditions, these solitons may form regular amplitude-ordered trains, irregular nonstationary ensembles of interacting localized structures, or stationary propagating multi-soliton complexes. We further demonstrate that soliton interactions in the Gardner-Ostrovsky equation are inherently inelastic, leading to the emergence of a dominant "soliton-champion" in closed systems. For example, under periodic boundary conditions, only the largest-amplitude soliton ultimately survives, while all smaller solitons are gradually eliminated through successive interactions. Despite their inelastic interactions, Gardner-Ostrovsky solitons exhibit remarkable robustness.
Comments24 pages, 16 figures
