Numerical comparison of mass-conservative schemes for the Gross-Pitaevskii equation [PDF]
Kinetic and Related Models, 2018 In this paper we present a numerical comparison of various mass-conservative discretizations for the time-dependent Gross-Pitaevskii equation. We have three main objectives.
P. Henning, Johan Warnegaard
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Turbulence in the two-dimensional Fourier-truncated Gross–Pitaevskii equation
New Journal of Physics, 2013 We undertake a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross–Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters.
Vishwanath Shukla +2 more
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Symmetry, 2020 We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (
A. V. Shapovalov +2 more
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On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT- and non- PT-symmetric potentials. [PDF]
Chaos, 2016 We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time- ( PT-) and non- PT-symmetric potentials.
Zhenya Yan, Yong Chen, Zichao Wen
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Instability of standing waves for the inhomogeneous Gross-Pitaevskii equation
AIMS Mathematics, 2020 In this paper, we consider the instability of standing waves for an inhomogeneous Gross-Pitaevskii equation \[ i\psi_t +\Delta \psi -a^2|x|^2\psi +|x|^{-b}|\psi|^{p}\psi=0. \] This equation arises in the description of nonlinear waves such as propagation
Yongbin Wang, Binhua Feng
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Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on $\mathbb {T}^{4}$
Forum of Mathematics, Pi, 2022 We consider the $\mathbb {T}^{4}$ cubic nonlinear Schrödinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross–Pitaevskii hierarchy, an uncommon method for NLS analysis which is ...
Xuwen Chen, Justin Holmer
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Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
International Journal of Differential Equations, 2013 We study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping.
Renato Colucci +2 more
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Polaron Dynamics in a Quasi-Two-Dimensional Bose–Einstein Condensate
Universe, 2023 The concept of polaron quasiparticles was first introduced in the pioneering papers by Landau and Feynman in the 1930s and 1940s. It describes the phenomenon of an external particle producing a bound state in an embedded medium.
Shukhrat N. Mardonov +3 more
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Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management
, 2008 In this paper we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential.
Abdullaev +39 more
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Bose-Einstein Condensates in the Large Gas Parameter Regime [PDF]
, 2001 Bose-Einstein condensates of 10$^4$ $^{85}$Rb atoms in a cylindrical trap are studied using a recently proposed modified Gross-Pitaevskii equation. The existence of a Feshbach resonance allows for widely tuning the scattering length of the atoms, and ...
A. Fabrocini +19 more
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