It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves.

它显示了如何通过使用Lax线性方程计算三次NLS（非线性Schrödinger）方程的双周期解的不稳定性率。双周期解的波函数模量在空间和时间坐标上都是周期性的。这样的解决方案推广了具有时间无关和空间周期波函数模量的驻波。与NLS方程中的其他波类似，双周期解在频谱上不稳定，这种不稳定性与虚轴外的Lax谱带有关。使用一种简单的数值方法来计算不稳定频谱，并比较双周期解和驻波的不稳定性。