Rogue Waves in the Generalized Derivative Nonlinear Schrodinger Equations
Rogue Waves in the Generalized Derivative Nonlinear Schrodinger Equations
复制标题
广义导数非线性薛定谔方程中的异常波
DOI：
10.1007/s00332-020-09643-8
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发表时间：
2020
影响因子：
3
通讯作者：
Yang Jianke
中科院分区：
文献类型：
--
作者：
Yang Bo;Chen Junchao;Yang Jianke
利用双线性Kadomtsev-Petviashvili（KP）约化方法导出了广义导数非线性薛定谔（GDNLS）方程的一般异常波.这些GDNLS方程包含Kaup-Newell方程、Chen-Lee-Liu方程和Gerdjikov-Ivanov方程作为特例。在这个双线性框架中，它表明，流氓波的所有成员，这些方程表示由相同的双线性解决方案。与以往的双线性KP约化方法相比，在我们目前的KP约化过程中的一个重要改进是一个新的参数化的内部参数的流氓波在其他可积方程的流氓波。在这种新的参数化下，用基本Schur多项式表示的异常波更为简单。此外，通过将所有内部参数设为零，可以得到各阶峰值振幅最大的异常波，且N阶峰值振幅的最大值是背景振幅的倍，与各阶GDNLS方程和背景波数无关。这些GDNLS方程可以分解成两个不同的双线性系统，这需要不同的KP减少，但产生的流氓波保持不变。文中还分析了GDNLS方程中异常波的动力学性质。结果表明，恒定背景的波数强烈地影响着流氓波的方向和持续时间。此外，还提出了一些新的流氓模式。
General rogue waves are derived for the generalized derivative nonlinear Schrödinger (GDNLS) equations by a bilinear Kadomtsev–Petviashvili (KP) reduction method. These GDNLS equations contain the Kaup–Newell equation, the Chen–Lee–Liu equation and the Gerdjikov–Ivanov equation as special cases. In this bilinear framework, it is shown that rogue waves to all members of these equations are expressed by the same bilinear solution. Compared to previous bilinear KP reduction methods for rogue waves in other integrable equations, an important improvement in our current KP reduction procedure is a new parameterization of internal parameters in rogue waves. Under this new parameterization, the rogue wave expressions through elementary Schur polynomials are much simpler. In addition, the rogue wave with the highest peak amplitude at each order can be obtained by setting all those internal parameters to zero, and this maximum peak amplitude at orderNturns out to betimes the background amplitude, independent of the individual GDNLS equation and the background wavenumber. It is also reported that these GDNLS equations can be decomposed into two different bilinear systems which require different KP reductions, but the resulting rogue waves remain the same. Dynamics of rogue waves in the GDNLS equations is also analyzed. It is shown that the wavenumber of the constant background strongly affects the orientation and duration of the rogue wave. In addition, some new rogue patterns are presented.