中俄数学啪啪啦
讨论班—Travelling waves in a three-layer fluid
报告人：Yakov Zhurenkov (Novosibirsk State University and Lavrentyev Institute of Hydrodynamics)
时间：2026-05-08 15:30-16:30
地点：智华楼四元厅
Abstract: Currently, the mathematical model of an ideal three-layer incompressible fluid attracts considerable attention in the study of nonlinear internal waves. This is due to the fact that, despite its relative simplicity, this model describes a fairly rich set of flow regimes that can be observed in nature and laboratory conditions. A special place among such regimes is occupied by a subclass of stratified flows described by the stationary equations of the second approximation of shallow water theory. Despite the large number of solutions of these equations obtained both analytically and numerically, the question of the qualitative behavior of wave structures in a three-layer flow remains insufficiently studied when its initial parameters are perturbed. In current report a procedure based on reducing the Hamilton’s equations to normal form by canonical transformations uses for constructing asymptotic solutions. Thus, in the neighbourhood of the parameters corresponding to the bifurcation point, it is possible to describe second-mode soliton with undamped oscillations at infinity and classical first-mode soliton. Additionally, the analysis of the conditions under which the term corresponding to quadratic non-linearity vanishes in the asymptotic equations is carried out. In this case solutions such as fronts connecting a pair of conjugate states appear in the system.
