Results 21 to 30 of about 1,617,542 (166)
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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Existence and properties of travelling waves for the Gross-Pitaevskii equation [PDF]
, 2008 This paper presents recent results concerning the existence and qualitative properties of travelling wave solutions to the Gross-Pitaevskii equation posed on the whole space R^N.
Philippe Gravejat +5 more
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Standing waves of the Anderson-Gross-Pitaevskii equation
In this paper, we study standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2. The Anderson-Gross-Pitaevskii equation is a nonlinear Schrödinger equation with a confining potential and a multiplicative spatial white noise ...
Mackowiak, Samaël
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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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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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Toward Coherent Polaritonic Devices Operating at Room Temperature
Nanophotonics, Volume 15, Issue 17, 11 September 2026.Polariton condensate formation and long‐range coherent transport is demonstrated using molecular exciton polaritons at room temperature (left). Waveguides and related photonic structures, such as Y‐splitters and interferometers, are realized via a focused ion beam etching of the planar microcavity. Coherent propagation of the condensate is demonstrated
Addhyaya Sharma +8 more
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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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Few‐Photon Fluorescence From Ultracold Bosons in an Optical Cavity
Contributions to Plasma Physics, Volume 66, Issue 7-8, September 2026.ABSTRACT Within a cavity quantum electrodynamics framework, we analyse the fluorescent spectrum of ultracold bosons in resonant and second‐harmonic generation (SHG) regimes. Two settings are considered: (i) (few) bosons in an optical lattice and (ii) a trapped two‐component dilute Bose–Einstein condensate (2BEC) within the Bogoliubov scheme.
Megha Gopalakrishna +2 more
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