Growth or decay of a coherent structure interacting with random waves,Physical Review E

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Growth or decay of a coherent structure interacting with random waves
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-15 , DOI: 10.1103/physreve.104.034213
Yuanting Chen ₁ , Benno Rumpf ₁

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Solitary waves interacting with random Rayleigh-Jeans distributed waves of a nonintegrable and noncollapsing nonlinear Schrödinger equation are studied. Two opposing types of dynamics are identified: First, the random thermal waves can erode the solitary wave; second, this structure can grow as a result of this interaction. These two types of behavior depend on a dynamical property of the solitary wave (its angular frequency), and on a statistical property of the thermal waves (the chemical potential). These two quantities are equal at a saddle point of the entropy that marks a transition between the two types of dynamics: high-amplitude coherent structures whose frequency exceeds the chemical potential grow and smaller structures with a lower frequency decay. Either process leads to an increase of the wave entropy. We show this using a thermodynamic model of two coupled subsystems, one representing the solitary wave and one for the thermal waves. Numerical simulations verify our results.

中文翻译：

与随机波相互作用的相干结构的生长或衰减

研究了孤立波与不可积分和非塌陷非线性薛定谔方程的随机瑞利-金分布波相互作用。确定了两种对立的动力学类型：首先，随机热波可以侵蚀孤立波；其次，这种结构可以因这种相互作用而增长。这两种类型的行为取决于孤立波的动力学特性（其角频率）和热波的统计特性（化学势）。这两个量在标志着两种动力学之间过渡的熵的鞍点处相等：频率超过化学势的高振幅相干结构增长，而较小的结构具有较低的频率衰减。任何一个过程都会导致波熵的增加。我们使用两个耦合子系统的热力学模型来展示这一点，一个代表孤立波，一个代表热波。数值模拟验证了我们的结果。

更新日期：2021-09-16

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