Abstract. We study the dynamics of the Schrödinger equation with a fractional Laplacian (−∆), and the decoherence of the solution is observed in certain cases. Analytically, we find equations describing the dynamics of the expected position and expected momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the Newtonian equations of motion for the non-...

We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general initial perturbation of the Kirchhoff ellipse are determined by the fastest growing mode for the correspo...

The present article represents part of the PhD. dissertation by C. Josserand1. We discuss the nucleation of quantized vortices in the nonlinear Schrödinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field ψ ...

On the basis of relationship between kinetic equation for two soliton clouds in theory Korteweg-de Vries and equations Chaplygin gas dynamics it is shown that existence waves propagating without a change their form fundamental property nonlinear gases. The solutions several typical problems are considered characteristic features such dynamics, which make possible to estimate effects interaction...

We report a numerical study of turbulence and Bose-Einstein condensation within the two-dimmensional GrossPitaevski model with repulsive interaction. In presence of weak forcing localized around some wave number in the Fourier space, we observe three qualitatively different evolution stages. At the initial stage a thermodynamic energy equipartition spectrum forms at both smaller and larger scal...