Exact analysis and elastic interaction of multi-soliton for a two-dimensional Gross-Pitaevskii equation in the Bose-Einstein condensation [PDF]
Journal of Advanced Research, 2022 Introduction: The Gross-Pitaevskii equation is a class of the nonlinear Schrödinger equation, whose exact solution, especially soliton solution, is proposed for understanding and studying Bose-Einstein condensate and some nonlinear phenomena occurring in
Haotian Wang, Qin Zhou, Wenjun Liu
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Quantum Gross-Pitaevskii Equation [PDF]
SciPost Physics, 2017 We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of ...
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
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Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation [PDF]
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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Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics.
Aleksandr L. Lisok +2 more
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Self-Consistent Derivation of the Modified Gross-Pitaevskii Equation with Lee-Huang-Yang Correction [PDF]
Applied Sciences, 2018 We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory, we derive a zero-temperature modified Gross–Pitaevskii equation with beyond-mean-field corrections due to quantum depletion ...
Luca Salasnich
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Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation [PDF]
Journal of Computational Physics, 2003 We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and obtain a four-
Weizhu Bao, Dieter Jaksch
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New Dynamics of the Classical and Nonlocal Gross-Pitaevskii Equation with a Parabolic Potential [PDF]
Reports on Mathematical Physics, 2020 Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double Wronskians. Solutions
Da-jun Zhang
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Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2005 The complex WKB-Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross-Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors.
Alexander Shapovalov +2 more
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Applied Mathematics Letters, 2019 A generalized nonlocal nonlinear Gross–Pitaevskii(GP) equation is presented, which can be reduced to the nonlocal GP equation with self-induced PT-symmetric potential.
Fajun yu
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Complex soliton wave patterns of Gross–Pitaevskii systems: application in quantum and optical engineering [PDF]
Scientific ReportsThe purpose of this work is to explore precise solutions, particularly soliton solutions, by fractionally analyzing the multicomponent Gross–Pitaevskii problem, a basic nonlinear Schrödinger equation. Soliton solutions are essential for comprehending the
Muhammad Bilal +5 more
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