Related papers: New perspectives on superfluidity in resonantly--d…
This paper presents a rigorous study of advanced functional spaces, with a focus on Sobolev and Besov spaces, to investigate key aspects of fluid dynamics, including the regularity of solutions to the Navier-Stokes equations, hypercomplex…
We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations. Firstly, we investigate the linear stability…
The piston shock problem is a prototypical example of strongly nonlinear fluid flow that enables the experimental exploration of fluid dynamics in extreme regimes. Here we investigate this problem for a nominally dissipationless, superfluid…
We consider turbulence in the Gross-Pitaevsky model and study the creation of a coherent condensate via an inverse cascade originated at small scales. The growth of the condensate leads to a spontaneous breakdown of symmetries of…
This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…
Acoustic horizons in Bose--Einstein condensates are usually characterized through long-wavelength Bogoliubov phonons. We study a nonlinear counterpart: whether a one-dimensional dark-soliton branch can sustain upstream laboratory motion in…
We study solutions of the one-dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms,…
Formation of oblique solitons by a flow of polariton condensate past an obstacle is considered. The flow is non-uniform due to a finite life-time of polaritons what changes drastically the conditions of formation of oblique solitons…
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
The study of superfluid quantum vortices has long been an important area of research, with previous work naturally focusing on two-dimensional and three-dimensional systems, where rotation stabilises point vortices and line vortices…
This paper represents the full version of a paper published earlier in Physica A [246 (1997), 275]. The present paper includes argumentation, proofs and details omitted in the shortened version. The papers are a further development of the…
Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero…
Semiconductor microcavity polaritons in the optical parametric scattering regime have been recently demonstrated to display a new variety of dissipationless superfluid behaviour. We report the first observation in resonantly pumped exciton…
Three-dimensional, Gross-Pitaevskii equation (GPE) simulations are presented of the interaction between neutron superfluid vortices and proton superconductor flux tubes in a rotating, harmonic trap, representing an idealised model of the…
In this article, we review the research on the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates. First, after briefly reviewing the earlier research and describing the current problems on quantized…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
Spin-superflow turbulence (SST) in spin-1 ferromagnetic spinor Bose-Einstein condensates is theoretically and numerically studied by using the spinor Gross-Pitaevskii (GP) equations. SST is turbulence in which the disturbed spin and…
We propose a dynamical protocol to generate supersolids in dipolar quantum gases by sweeping a repulsive Gaussian barrier through an incoherent quasi-one-dimensional droplet array. Supersolidity is inferred by monitoring the ensuing…