Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Abstract

We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate of modulation instability is maximal. An envelope solitary wave of this frequency can be described by the conventional nonlinear Schrödinger equation. A soliton solution to this equation is presented for the time-like version of the nonlinear Schrödinger equation. When such envelope soliton enters a coastal zone where the bottom gradually linearly increases, then it experiences an adiabatical transfor-arXiv:1903.07817v2 [physics.flu-dyn] 22 Mar 2019mation. This leads to an increase of soliton amplitude, velocity, and period of a carrier wave, whereas its duration decreases. It is shown that the soliton becomes taller and narrower. At some distance it looks like a breather, a narrow nonstationary solitary wave. The dependences of soliton parameters on the distance when it moves towards the shoaling are found from the conservation laws and analysed graphically. Estimates for the real ocean are presented.

Nonlinear Schrodinger Equation Solitons on Quantum Droplets

“…At lab scale, the formation of periodic nonlinear waves, or cnoidal waves for Korteweg-de Vries models (KdV), on closed and bounded systems was detected and the results were matched with theoretical calculations in low temperature interfacial systems [35,40], in confined rotating flows [28], and along circular chains of magnetic pendulums [29]. Experiments demonstrate the formation of rotating hollow polygons in 2D fluids, within good match with theoretical models of cnoidal waves [39][40][41][42][43][44][45][46][47].…”