参数驱动非线性薛定谔方程中椭圆余弦波的稳定性
Stability of cnoidal waves in the parametrically driven nonlinear Schrödinger equation
摘要：
参数驱动的阻尼非线性薛定谔方程有两个cn波解和两个dn波解。我们表明，一对CN和DN的解决方案是不稳定的驱动程序的强度，耗散系数和波的空间周期的任何组合，这种不稳定性是对周期性扰动。第二个dn波解在参数空间的某个区域内对反周期扰动是不稳定的。我们还考虑了长调制波长的准周期扰动，在驱动强度仅弱超过阻尼系数的极限。
英文摘要：
The parametrically driven, damped nonlinear Schrödinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and spatial period of the wave; this instability is against periodic perturbations. The second dn-wave solution is shown to be unstable against antiperiodic perturbations --- in a certain region of the parameter space. We also consider quasiperiodic perturbations with long modulation wavelength, in the limit where the driving strength is only weakly exceeding the damping coefficient.
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