Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.
Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.
复制标题
DOI：
10.1103/physreve.92.012917
复制
发表时间：
2015-07
期刊：
影响因子：
--
通讯作者：
Xiaoyong Wen;Yunqing Yang;Zhenya Yan
中科院分区：
文献类型：
--
作者：
Xiaoyong Wen;Yunqing Yang;Zhenya Yan
利用行列式的分数次形式，给出了一种求修正的非线性薛定谔(MNLS)方程的广义摄动(n，M)重达布变换(DT)的简单而有意义的方法。特别地，我们应用广义摄动(1，N-1)重离散方程来求其显式多流氓波解。详细讨论了不同参数下MNLS方程的这些流氓波解的波结构，显示了丰富的有趣的波结构，包括三角形和五边形等，这可能有助于研究光学中多流氓波的物理机制。通过数值模拟说明了这些多流氓波解的动力学行为。同样的Darboux矩阵也可以用来研究Gerjikov-Ivanov方程，从而找到它的多流氓波解及其波结构。该方法还可以推广到求解其他非线性可积方程的多流氓波解。
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.