基于高阶非线性修正Frenkel-Kontorova模型的调制不稳定性增益与局域波
Modulation instability gain and localized waves by modified Frenkel-Kontorova model of higher order nonlinearity
AI总结：
本文通过多尺度方法和线性化方案研究含三次-四次非线性项的修正Frenkel-Kontorova一维原子链模型，揭示了高阶非线性对调制不稳定性增益的影响，并通过非线性超传输现象观察到亮孤子、调制波及孤子混沌化行为，证明该模型是产生长寿命调制波的有效平台。
摘要：
本文利用三次-四次非线性系数研究一维原子链中的调制不稳定性和非线性超传输现象。通过多尺度方法，我们建立了离散非线性演化方程。为了计算调制不稳定性增益，采用了线性化方案，并特别关注高阶非线性项对调制不稳定性的影响。随后，进行完全数值积分以识别调制波型以及怪波的出现。通过非线性超传输现象，将离散模型的一端驱动到禁带中。结果表明，当驱动幅度超过超传输阈值时，可以满足亮孤子和调制波型的产生条件。在传播的瞬态时间范围内观察到一种重要行为：亮孤子波转变为混沌孤子波。这些结果证实了我们对调制不稳定性的解析研究，并表明一维原子链是产生长寿命调制波的有效介质。
英文摘要：
In this paper, modulation instability and nonlinear supratransmission are investigated in a one-dimensional chain of atoms using cubic-quartic nonlinearity coefficients. As a result, we establish the discrete nonlinear evolution equation by using the multi-scale scheme. To calculate the modulation instability gain, we use the linearizing scheme. Particular attention is given to the impact of the higher nonlinear term on the modulation instability. Following that, full numerical integration was performed to identify modulated wave patterns, as well as the appearance of a rogue wave. Through the nonlinear supratransmission phenomenon, one end of the discrete model is driven into the forbidden bandgap. As a result, for driving amplitudes above the supratransmission threshold, the solitonic bright soliton and modulated wave patterns are satisfied. An important behavior is observed in the transient range of time of propagation when the bright solitonic wave turns into a chaotic solitonic wave. These results corroborate our analytical investigations on the modulation instability and show that the one-dimensional chain of atoms is a fruitful medium to generate long-lived modulated waves.
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