相关论文: Evolution of rarefaction pulses into vortex rings
Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary…
The rotation modified Kadomtsev Petviashvili equation which is also known as the Kadomtsev Petviashvili Ostrovsky equation, describes the gradual wave field diffusion in the transverse direction to the direction of the propagation of the…
We study the generalized point-vortex problem and the Gross-Pitaevskii equation on surfaces of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two two rings of $n$ equally spaced vortices…
We have investigated the nonlinear amplitude vector equation governing the evolution of optical pulses in optical and UV region. We are normalizing this equation for the cases of different and equal transverse and longitudinal size of…
We study the resolution of discontinuous singularities in gas dynamics via multi-dimensional rarefaction waves. While the mechanism is well-understood in one spatial dimension, the rigorous construction in higher dimensions has remained a…
We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential, and forced by shaking along one axis. We observe the development of isotropic turbulence from…
Quantized vortices have been observed in a variety of superfluid systems, from $^4$He to condensates of alkali-metal bosons and ultracold Fermi gases along the BEC-BCS crossover. In this article we study the stability of singly quantized…
Using variational methods, we construct approximate solutions for the Gross-Pitaevski equation which concentrate on circles in $\R^3$. These solutions will help to show that the $L^2$ flow is unstable for the usual topology and for the…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…
Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold…
In this work we are interested in extreme vortex states leading to the maximum possible growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This study is a part of a broader research effort motivated by the…
We study the transverse spectral stability of the one-dimensional small-amplitude periodic traveling wave solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky (KD) equation. We show that these waves are transversely unstable with…
Three coaxial quantized vortex rings in a Bose-Einstein condensate exhibit aperiodic leapfrogging dynamics. It is found that such circular vortex rings are dynamically unstable against deformation breaking axial rotational symmetry. The…
As is well-known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices respectively. Recently, we have studied how, in a hypothetical…
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…
We present numerical solutions of the Gross--Pitaevskii equation corresponding to reconnecting vortex lines. We determine the separation of vortices as a function of time during the approach to reconnection, and study the formation of…
The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93}, 160406 (2004)] on the decay of a doubly quantized vortex imprinted in $^{23}% $Na condensates is analyzed by numerically solving the Gross-Pitaevskii equation.…