For the parametrically driven nonlinear Schrödinger equation, two criteria for the dynamical stability of solitons are presented, using the driving force f ( x , t ) = a exp[2 i K ( t ) x ]. Both criteria are based on the results of a collective coordinate theory. In this theory, the parameters of the 1-soliton solution are allowed to depend on time and a variational approach yields a set of coupled nonlinear ODEs for the collective coordinates. The solutions of these ODEs are used to compute the soliton’s normalized momentum p ( t ), velocity v ( t ), and a parametric plot p ( v ). The first criterion states that a sufficient condition for instability is fulfilled if the curve p ( v ), or a piece of it, has a negative slope. If the slope is positive then a necessary condition for stability is fulfilled. For constant K , a second criterion is presented. Here a complex wave...

中文翻译：

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非线性Schrödinger方程的参数驱动孤子的经验稳定性准则

对于参数驱动的非线性Schrödinger方程，使用驱动力f（x，t）= a exp [2 i K（t）x]提出了两个孤子动力学稳定性的标准。这两个标准都是基于集体坐标理论的结果。在该理论中，允许1-孤子解的参数取决于时间，并且采用变分方法可生成一组耦合的集体坐标的非线性ODE。这些ODE的解用于计算孤子的归一化动量p（t），速度v（t）和参数图p（v）。第一个标准指出，如果曲线p（v）或其一部分具有负斜率，则满足不稳定性的充分条件。如果斜率为正，则满足稳定性的必要条件。对于常数K，提出了第二个标准。这是一个复杂的浪潮...