Related papers: Nonlinear Schr\"odinger Equation for Superconducto…
We perform the analysis of the focusing nonlinear Schr\"odinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of B\"acklund transformations. The difficulty…
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…
It is shown for the Bose-Einstein condensate of cold atomic system that the new unperturbed Hamiltonian, which includes not only the first and second powers of the zero mode operators but also the higher ones, determines a unique and…
We study the properties of the ground state of Nonlinear Schr\"odinger Equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same…
The properties of the superfluid phase of ultra cold bosonic atoms loaded in a circular array are investigated in the framework of the Bose-Hubbard model and the Bogoliubov theory. We derive and solve the Gross-Pitaevskii equation of the…
A nonlinear Schr\"odinger equation is derived for the dynamics of a beam of ultracold fermionic atoms traversing a Bose-Einstein condensate. The condensate phonon modes are shown to provide a nonlinear medium for the fermionic atoms. A…
Oleinik's \emph{no back-flow} condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain $R\subset \mathbb{R}^2$. It also allowed us to find a limit formula for Dorodnitzyn's stationary…
At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined…
In the preceding papers the present author gave another proof of the existence and uniqueness of the solution to the BCS-Bogoliubov gap equation for superconductivity from the viewpoint of operator theory, and showed that the solution is…
We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
The modulational instability of spatially uniform states in the nonlinear Schr\"odinger equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in…
The Schr\"odinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, $m$ being the boson mass, the equations have been postulated to approximate…
A Bose-Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical…
We investigate the behavior of an array of Bose-Einstein condensate tubes described by means of a Bose-Hubbard Hamiltonian. Using an anisotropic non-polynomial Schrodinger equation we link the macroscopic parameters in the Bose-Hubbard…
The thermodynamics of the discrete nonlinear Schr\"odinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a…
Considering both the power Maxwell invariant source and the Einstein--Gauss--Bonnet gravity, we present a new class of static solutions yields a spacetime with a longitudinal nonlinear magnetic field. These horizonless solutions have no…
We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an…
We present an exact analytic solution of a nonlinear Schr\"odinger field interacting with a moving potential (obstacle) at supersonic speed. We show that the field forms a stable shape-invariant structure localized around the obstacle --- a…
We consider the nonlinear Schr\"odinger equations with a potential on $\mathbb T^d$. For almost all potentials, we show the almost global stability in very high Sobolev norms. We apply an iteration of the Birkhoff normal form, as in the…