论文标题
在四阶非线性schrödinger方程中单个和双周期波的不稳定性
Instability of single- and double-periodic waves in the fourth-order nonlinear Schrödinger equation
论文作者
论文摘要
我们计算了四阶非线性schrödinger方程的单个和双周期波解的不稳定性速率。四阶非线性Schrödinger方程的单周期和双周期解决方案是根据Jacobian椭圆函数（例如$ dn $，$ cn $和$ sn $）得出的。从光谱问题中，我们计算单个波波的宽松和稳定光谱。然后，我们计算单周期波的不稳定性速率（空间变量中的周期性）。我们还获得了椭圆模量参数不同值的双周期波解的宽松和稳定谱。我们还重点介绍了考虑系统展示的某些新颖功能。然后，我们计算了系统参数不同值的两个双周期溶液的两个家族的不稳定性率。我们的结果表明，与单周期波相比，由于四阶分散参数，双周期波的不稳定性生长速率更高。
We compute the instability rate for single- and double-periodic wave solutions of a fourth-order nonlinear Schrödinger equation. The single- and double-periodic solutions of a fourth-order nonlinear Schrödinger equation are derived in terms of Jacobian elliptic functions such as $dn$, $cn$, and $sn$. From the spectral problem, we compute Lax and stability spectrum of single-periodic waves. We then calculate the instability rate of single-periodic waves (periodic in the spatial variable). We also obtain the Lax and stability spectrum of double-periodic wave solutions for different values of the elliptic modulus parameter. We also highlight certain novel features exhibited by the considered system. We then compute instability rate for two families of double-periodic wave solutions of the considered equation for different values of the system parameter. Our results reveal that the instability growth rate is higher for the double-periodic waves due to the fourth-order dispersion parameter when compared to single-periodic waves.
