Congy T, El G A, Roberti G, Tovbis A, Randoux S, Suret P
Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom.
Department of Mathematics, University of Central Florida, Orlando, Florida 32816, USA.
Phys Rev Lett. 2024 May 17;132(20):207201. doi: 10.1103/PhysRevLett.132.207201.
We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schrödinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular nonbound state gas is considered, providing important insights related to the validity of the so-called virial theorem.
我们使用孤子气体的光谱动力学理论来研究由一维聚焦非线性薛定谔方程（fNLSE）描述的可积湍流中极端事件的可能性。通过对fNLSE的逆散射变换进行随机解释，并根据相应孤子气体的态密度谱来解析评估新兴随机非线性波场的峰度，从而实现这一目标。然后，我们将这一通用结果应用于可积湍流产生的两种基本情形：（i）平面波自发调制不稳定性的渐近发展，以及（ii）强非线性、部分相干波的长时间演化。在这两种涉及束缚态孤子气体动力学的情况下，解析得到的峰度值与从fNLSE的直接数值模拟推断出的值完全一致，为各自的 rogue 波统计提供了期待已久的理论解释。此外，还考虑了一种特定非束缚态气体的演化，为所谓的维里定理的有效性提供了重要见解。
