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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Rogue waves in higher-order systems: Lagrangian approach
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Rogue waves in higher-order systems: Lagrangian approach

机译：Rogue Wave在高阶系统：拉格朗日方法

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摘要

A Lagrangian approach for finding rogue wave solutions of the extended nonlinear Schrodinger equation system is developed. A list of Lagrangian components for a variety of terms in the extended equation is presented. It turns the analysis of any equation into a simple and straightforward exercise. The fact that these terms can be summed is a major point in achieving this simplicity. Importantly, the technique provides the same result, no matter whether an extension term enters the basic part of the equation or is taken as a perturbation. This significant conclusion is demonstrated by giving several examples. We give several examples of the application of this technique for particular physically-relevant extended equations. As a typical example, the Lagrangian approach is used to evaluate the effects of fourth and sixth order dispersion on rogue waves. The results are compared with solutions found by numerical simulations of the original equation. Good agreements are found, thus confirming the usefulness of the approach. A generalization to even higher-order dispersive terms shows that the phase function for the rogue wave can be written in terms of known functions, e.g. the arcsinh function. When these equations are integrable, the solutions naturally coincide with the exact rogue wave solutions. Obtaining the exact solution this way is demonstrated in the case of Kundu-Echkaus equation.
机译：开发了一种用于查找延长非线性薛定兆式系统的罗格波解决方案的拉格朗日方法。提出了扩展方程中各种术语的拉格朗日组件列表。它将任何方程分析到简单而直接的运动中。这些术语可以总结这些术语是实现这一简单性的重要意义。重要的是，无论扩展术语是否进入等式的基本部分，都提供了相同的结果，或者被视为扰动。通过给出几个例子，证明了这一重要的结论。我们提供了几个针对特定物理相关的扩展方程式应用该技术的示例。作为一个典型的例子，拉格朗日方法用于评估第四和第六阶分散对流氓波的影响。将结果与原始方程的数值模拟发现的解决方案进行了比较。发现了良好的协议，从而确认了这种方法的有用性。甚至高阶分散术语的概括表明，可以根据已知功能编写流浪波的相位函数，例如， Arcsinh函数。当这些等式是可集成的时，解决方案自然与精确的流氓波解决方案相一致。在Kundu-echkaus方程的情况下，证明了以这种方式获得确切的解决方案。

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