Related papers: Soliton-phonon scattering problem in 1D nonlinear …
It is shown that the one-dimensional nonlinear Schr\"odinger equation with a dissipative periodic potential, nonlinear losses and linear pump allow for the existence of stable nonlinear Bloch states which are attractors. The model describes…
Solutions to the phonon Boltzmann transport equation under the relaxation-time approximation (RTA) are fundamentally limited in that they do not account for the off-diagonal elements of the scattering matrix, which encode intermode energy…
This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schr\"odinger equations. The nonlinearity includes a non-oscillatory term of the order lower than the Strauss exponent. We show that no…
In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is…
We consider a quantum above-barrier reflection of a Bose-Einstein condensate by a one-dimensional rectangular potential barrier, or by a potential well, for nonlinear Schroedinger equation (Gross-Pitaevskii equation) with a small…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
The occurrence of a molecular Bose-Einstein condensate is studied for an atomic system near a zero energy resonance of the binary scattering process, with a large and positive scattering length. The interaction potential is modeled by a…
The Gross-Pitaevskii equation, or more generally the nonlinear Schr\"odinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the…
Solitons confined in a channel are studied in the two-dimensional nonlinear Schroedinger equation. When a channel branches into two channels, a soliton is split into two solitons, if the initial kinetic energy exceeds a critical value. The…
In this paper, we develop an inverse scattering transform for the integrable focusing nonlinear Schr\"odinger (NLS) equation on the half-line subject to a class of boundary conditions. The method is based on the notions of integrable…
We present a comprehensive theoretical study of linear wave scattering from magnetic domain walls with varied twist angles $\Theta$ in spin-$1/2$ Bose-Einstein condensates (BECs). Using a gauge transformation, we show that scattering…
We study a two-component nonlinear Schr{\"{o}}dinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating…
Phonon-like excitations can be imprinted into a trapped Bose-Einstein condensate of cold atoms using light scattering. If the condensate is suddenly let to freely expand, the initial phonons lose their collective character by transferring…
The behavior of the momentum transferred to a trapped Bose-Einstein condensate by a two-photon Bragg pulse reflects the structure of the underlying Bogoliubov spectrum. In elongated condensates, axial phonons with different number of radial…
We consider a class of biharmonic nonlinear Schr\"odinger equations with a focusing inhomogeneous power-type nonlinearity \[ i\partial_t u -\Delta^2 u+\mu\Delta u +|x|^{-b} |u|^\alpha u=0, \quad \left. u\right|_{t=0}=u_0 \in…
We show soliton solutions of nonlinear Schroedinger equation on simple networks consisting of vertices and bonds, where the strength of cubic nonlinearity is different from bond to bond. We concentrate on reflectionless propagation of…
We study a discrete nonlinear Schr\"odinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and…
We observe nonlinear scattering of 39 K atomic bright solitons launched in a one-dimensional (1D) speckle disorder. We directly compare it with the scattering of non-interacting particles in the same disorder. The atoms in the soliton tend…
We study the Hartree-Fock-Bogoliubov mean-field theory as applied to a two-dimensional finite trapped Bose gas at low temperatures and find that, in the Hartree-Fock approximation, the system can be described either with or without the…
We investigate the Manakov model or, more generally, the vector nonlinear Schr\"odinger equation on the half-line. Using a B\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet…