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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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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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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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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Derivation of the Time Dependent Gross-Pitaevskii Equation in Two Dimensions. [PDF]
Commun Math Phys, 2019 We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting from an interacting N-particle system of bosons. We consider the interaction potential to be given either
Jeblick M, Leopold N, Pickl P.
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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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Evolution of Bose–Einstein condensate systems beyond the Gross–Pitaevskii equation [PDF]
Frontiers in Physics, 2023 While many phenomena in cold atoms and other Bose–Einstein condensate (BEC) systems are often described using the mean-field approaches, understanding the kinetics of BECs requires the inclusion of particle scattering via the collision integral of the ...
Yuli Lyanda-Geller, Yuli Lyanda-Geller
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Multi-vortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials [PDF]
SIAM Journal on Mathematical Analysis, 2018 For $N\leq34,$ we construct traveling waves with small speed for the Gross-Pitaevskii equation, by gluing $N(N+1)/2$ pairs of degree $\pm1$ vortices of the Ginzburg-Landau equation.
Yong Liu, Juncheng Wei
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Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials. [PDF]
Sci Rep, 2017 We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows
Li L, Yu F.
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