论文标题
有限的差距方法和定期的库奇问题$ 2+1 $ dimensional Anomalous Wave for focusing Davey-Stewartson 2方程
The finite gap method and the periodic Cauchy problem of $2+1$ dimensional anomalous waves for the focusing Davey-Stewartson 2 equation
论文作者
论文摘要
焦点非线性schrödinger（NLS）方程是描述弱非线性介质中的调制不稳定性（MI）的最简单通用模型（MI），MI被认为是自然界（AWS）波（AWS）的主要物理机制。与最近开发的焦点NLS方程定期AWS的分析理论类似，在本文中，我们将这些结果扩展到$ 2+1 $尺寸的上下文，重点关注焦点Davey-Stewartson 2（DS2）方程，这是一种集成的$ 2+1+1+1 $ dimens focus focus focusing NLS方程的尺寸。更确切地说，我们使用有限的差距理论来解决，领导秩序，这是对不稳定背景解决方案的小初始扰动的偶然周期性的cauchy问题，我们称之为AWS的周期性库奇问题。与NLS情况一样，我们表明，对于领先顺序，该问题的解决方案是根据初始数据的基本功能表示的。
The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of $1+1$ dimensional quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism for the appearence of anomalous (rogue) waves (AWs) in nature. In analogy with the recently developed analytic theory of periodic AWs of the focusing NLS equation, in this paper we extend these results to a $2+1$ dimensional context, concentrating on the focusing Davey-Stewartson 2 (DS2) equation, an integrable $2+1$ dimensional generalization of the focusing NLS equation. More precisely, we use the finite gap theory to solve, to leading order, the doubly periodic Cauchy problem of the focusing DS2 equation for small initial perturbations of the unstable background solution, what we call the periodic Cauchy problem of the AWs. As in the NLS case, we show that, to leading order, the solution of this Cauchy problem is expressed in terms of elementary functions of the initial data.
