Dysthe方程的相动力学与平面波的分叉
Phase Dynamics of the Dysthe equation and the Bifurcation of Plane Waves
摘要：
在Dysthe方程中研究了平面波到局部结构的分叉，该方程包含了平均流和波陡化的影响。通过使用相位调制技术，它表明，这种情况下可以使用Korteweg -德弗里斯（KdV）方程描述。该系统的孤立波解形成了分叉动力学的定性原型，然后通过它们如何进入这些孤立波的振幅和宽度来明确平均流和陡峭化的作用。此外，高阶相动力学的研究，导致增加的非线性制度，这反过来又有一个更深刻的影响如何在相位缺陷下的平面波变换。
英文摘要：
The bifurcation of plane waves to localised structures is investigated in the Dysthe equation, which incorporates the effects of mean flow and wave steepening. Through the use of phase modulation techniques, it is demonstrated that such occurrences may be described using a Korteweg - de Vries (KdV) equation. The solitary wave solutions of this system form a qualitative prototype for the bifurcating dynamics, and the role of mean flow and steepening is then made clear through how they enter the amplitude and width of these solitary waves. Additionally, higher order phase dynamics are investigated, leading to increased nonlinear regimes which in turn have a more profound impact on how the plane waves transform under defects in the phase.
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