Related papers: Two-dimensional stationary soliton gas
In two dimensions the Gross-Pitaevskii equation for a cold, dilute gas of bosons has an energy dependent coupling parameter describing particle interactions. We present numerical solutions of this equation for bosons in harmonic traps and…
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit…
Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons…
We study dimension reduction for the three-dimensional Gross-Pitaevskii equation with a long-range and anisotropic dipole-dipole interaction modeling dipolar Bose-Einstein condensation in a strong interaction regime. The cases of disk…
We investigate the dynamics of vector solitons in a two-component Bose-Einstein condensates governed by the system of Gross-Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze their…
In the paper, we study the plane Couette flow of a rarefied gas between two parallel infinite plates at $y=\pm L$ moving relative to each other with opposite velocities $(\pm \alpha L,0,0)$ along the $x$-direction. Assuming that the…
We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann-Vlasov equation with contact interaction, we derive an…
We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially…
Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths $\xi_1$ and $\xi_2$ and by…
We classify the Lie point symmetries for the 2+1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible f(u) functional forms where the latter depends. For each case the one-dimensional optimal system is…
We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the…
We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…
We consider the kinetic transport equation that arise in the Boltzmann-Grad limit of the two-dimensional periodic Lorentz Gas. This equation has been obtained by extending the phase space of positions and velocities through the introduction…
We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
We consider an ensemble of mass collisionless particles, which interact mutually either by an attraction of Newton's law of gravitation or by an electrostatic repulsion of Coulomb's law, under a background downward gravity in a…
The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this…
A fluid is said to be \emph{scale-invariant} when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry…
In the framework of coupled 1D Gross-Pitaevskii equations, we explore the dynamics of a binary Bose-Einstein condensate where the intra-component interaction is repulsive, while the inter-component one is attractive. The existence regimes…
We study the stability of gap solitons of the super-Tonks-Girardeau bosonic gas in one-dimensional periodic potential. The linear stability analysis indicates that increasing the amplitude of periodic potential or decreasing the nonlinear…