论文标题
带有两个不同双周期背景的流氓波及其五阶非线性schrödinger方程的模量不稳定性
Rogue waves with two different double-periodic wave backgrounds and their modulational instabilities of a fifth-order nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，我们在双周期波背景上得出了五阶非线性schrödinger方程的Rogue Wave（RW）溶液。在Darboux转换的首次迭代中，选择椭圆函数（$ CN $，$ DN $和$ SN $的组合）作为种子解决方案，并利用LAX对程序的非线性化，为第五阶非linelearearearearearearearearearearearearearearearearearearearkinger方程创建了双层型波浪背景。通过引入第二个线性独立的解决方案，我们在三个不同特征值的创建背景上生成了RW解决方案。我们证明了由于低阶和高阶分散项而导致的RW出现中发生的差异。我们详细研究了某些系统和椭圆模量参数值的派生解决方案，并突出了我们从研究中获得的一些有趣的特征。我们还计算了不同椭圆模量参数值下的双周期溶液不稳定性的增长率。
In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schrödinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the first iteration of Darboux transformation and utilizing the nonlinearization of Lax pair procedure, we create the double-periodic wave background for the fifth-order nonlinear Schrödinger equation. By introducing the second linearly independent solution, we generate the RW solutions on the created background for three different eigenvalues. We demonstrate the differences that occur in the appearance of RWs due to the lower-order and higher-order dispersions terms. We examine the derived solution in detail for certain system and elliptic modulus parameters values and highlight some interesting features that we obtain from our studies. We also calculate the growth rate for instability of double-periodic solutions under different values of elliptic modulus parameter.
