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Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping [PDF]
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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Comparison of Splitting Methods for Deterministic/Stochastic Gross–Pitaevskii Equation
Mathematical and Computational Applications, 2019 In this paper, we discuss the different splitting approaches to numerically solvethe Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einsteincondensate (BEC).
Jürgen Geiser, Amirbahador Nasari
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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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Nonlinear quantum search using the Gross–Pitaevskii equation
New Journal of Physics, 2013 We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross–Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision.
David A Meyer, Thomas G Wong
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Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation
Physical Review Research, 2019 Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion, and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound droplets, comparing ...
Fabian Böttcher +10 more
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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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Journal of Taibah University for ScienceBased on the generalized model of the cubic-quintic Gross-Pitaevskii equation with polytropic approximation, we novelly utilize an F-expansion method to identify bright soliton dynamics of systems modelled by the cubic-quintic Gross-Pitaevskii with ...
Qingru Wang +3 more
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Remarks on the Blow-Up Solutions for the Critical Gross-Pitaevskii Equation
Abstract and Applied Analysis, 2013 This paper is concerned with the blow-up solutions of the critical Gross-Pitaevskii equation, which models the Bose-Einstein condensate. The existence and qualitative properties of the minimal blow-up solutions are obtained.
Xiaoguang Li, Chong Lai
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Comparison of finite‐difference schemes for the Gross‐Pitaevskii equation
Mathematical Modelling and Analysis, 2009 A conservative finite‐difference scheme for numerical solution of the Gross‐Pitaevskii equation is proposed. The scheme preserves three invariants of the problem: the L 2 norm of the solution, the impulse functional, and the energy functional.
Vyacheslav A. Trofimov, Nikolai Peskov
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Results in Physics, 2021 A 3D nonautonomous partially nonlocal coupled Gross–Pitaevskii equation is paid attention under a linear potential. The similarity reduction from a 3D nonautonomous coupled equation into an autonomous one is implemented.
Jing Yang +4 more
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