Congy T, El G A, Roberti G, Tovbis A
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.
J Nonlinear Sci. 2023;33(6):104. doi: 10.1007/s00332-023-09940-y. Epub 2023 Sep 19.
We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg-de Vries (KdV) equation in the special "condensate" limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the -phase KdV-Whitham modulation equations derived by Flaschka et al. (Commun Pure Appl Math 33(6):739-784, 1980) and Lax and Levermore (Commun Pure Appl Math 36(5):571-593, 1983). We consider Riemann problems for soliton condensates and construct explicit solutions of the kinetic equation describing generalized rarefaction and dispersive shock waves. We then present numerical results for "diluted" soliton condensates exhibiting rich incoherent behaviors associated with integrable turbulence.
我们考虑在特殊的“凝聚态”极限下，Korteweg - de Vries（KdV）方程的非平衡致密孤子气体的大规模动力学。我们证明，在此极限下，态谱密度的积分 - 微分动力学方程简化为Flaschka等人（《纯粹与应用数学通讯》33(6):739 - 784, 1980）以及Lax和Levermore（《纯粹与应用数学通讯》36(5):571 - 593, 1983）所推导的 - 相KdV - Whitham调制方程。我们考虑孤子凝聚体的黎曼问题，并构造描述广义稀疏波和色散激波的动力学方程的显式解。然后，我们给出了“稀释”孤子凝聚体的数值结果，这些结果展现出与可积湍流相关的丰富的非相干行为。
