论文标题
Korteweg-De Vries方程的孤子冷凝物的分散性流体动力学
Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
论文作者
论文摘要
我们考虑特殊“冷凝水”极限中的Korteweg-De Vries（KDV）方程的非平衡密度孤子气体的大规模动力学。我们证明，在这种限制下，状态的光谱密度的全差异动力学方程将减少到$ n $ phase KDV-WHITHAM调制方程，该方程由Flaschka，Forest和McLaughlin（1980）以及Lax和Lax and Levermore（1983）得出。我们考虑了孤子冷凝物的利曼问题，并构建了描述广义稀疏和分散冲击波的动力学方程的显式解决方案。然后，我们提出了“稀释”的孤子冷凝水的数值结果，这些冷凝物表现出与湍流相关的丰富不相干行为。
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 $N$-phase KdV-Whitham modulation equations derived by Flaschka, Forest and McLaughlin (1980) and Lax and Levermore (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 behaviours associated with integrable turbulence.
