AI 中文总结
该研究在Kaup-Boussinesq方程框架下，通过引入高波数耗散扰动，发现弱耗散结合随机波可诱导浅水波中冠军孤子形成，为异常波形成提供了新机制。
AI 中文摘要
本文确定了浅水环境中异常波形成的一种新机制。我们在Kaup-Boussinesq方程的框架下研究双向浅水波场，并引入弱高波数耗散扰动，该扰动破坏了系统潜在的可积性。在该设定下，主导孤子通过与较弱的同向传播孤子的连续相互作用而增长，从而在每个传播方向上形成“冠军孤子”。这种行为与耗散会抑制相干结构的普遍直觉相反，反而表明弱耗散可诱导相干结构增强。此外，我们发现仅弱耗散不足以形成冠军孤子；随机波的存在在增强过程中起着关键作用，催化能量向主导相干结构的转移。尽管此前已在非可积系统中研究过冠军孤子，但这些工作主要考虑通过修改非线性项引入的扰动（例如高阶Korteweg-de Vries和Schrödinger型模型）。在本研究中，高波数耗散提供了一种更符合物理实际的扰动，因为这种小尺度阻尼是许多系统的共同特征。
英文摘要
In this paper, we identify a new mechanism for rogue wave formation in a shallow-water setting. We study a bidirectional shallow-water wave field in the context of the Kaup-Boussinesq equation, and introduce a weak high-wavenumber dissipative perturbation that breaks the underlying integrability of the system. In this setting, dominant solitons grow through successive interactions with weaker, co-propagating solitons, leading to the formation of a "champion soliton" in each direction of propagation. This behaviour is in contrast to the general intuition that dissipation damps coherent structures, and instead shows that weak dissipation can induce their intensification. Moreover, we find that weak dissipation alone is not sufficient for champion soliton formation; the presence of random waves plays a crucial role in the intensification process, catalysing the transfer of energy into dominant coherent structures. While champion solitons have previously been studied in non-integrable systems, these works primarily consider perturbations introduced through modifications of the nonlinear terms (e.g., higher-order Korteweg-de Vries and Schrödinger-type models). In the present work, high-wavenumber dissipation provides a more physically natural perturbation, since such small-scale damping is a common feature in many systems.
