非线性薛定谔方程中二阶孤子对扰动的稳定与失稳
Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schrödinger equation
摘要：
我们考虑了基于非线性薛定谔方程（NLSE）和弱共振非线性管理（NLM）的模型中二阶孤子（2-孤子呼吸子）的分裂和稳定，其中NLSE包含一个小的五次项，即，时间周期调制的立方系数，在频率接近的2孤子的形状振荡。该模型适用于具有五阶光学非线性和线性损耗与增益周期性交替的介质中的光传输，也适用于BEC，自聚焦五阶项解释了动力学对一维性的微弱偏离，而NLM可以通过费什巴赫共振诱导。我们提出了一个解释的2-孤子的共振分裂的影响下的NLM的作用。然后，使用系统的模拟和分析的方法，我们得出结论，弱五次非线性与自聚焦符号稳定的2-孤子，而自散焦五次非线性加速其分裂。它还表明，自散焦/聚焦符号的五次项使得2-孤子的共振响应的NLM基本上更广泛的，在频率方面。
英文摘要：
We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schrödinger equation (NLSE), which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagation in media with cubic-quintic optical nonlinearities and periodic alternation of linear loss and gain, and to BEC, with the self-focusing quintic term accounting for the weak deviation of the dynamics from one-dimensionality, while the NLM can be induced by means of the Feshbach resonance. We propose an explanation to the effect of the resonant splitting of the 2-soliton under the action of the NLM. Then, using systematic simulations and an analytical approach, we conclude that the weak quintic nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the self-defocusing quintic nonlinearity accelerates its splitting. It is also shown that the quintic term with the self-defocusing/focusing sign makes the resonant response of the 2-soliton to the NLM essentially broader, in terms of the frequency.
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