Special solutions of the Riccati equation with applications to the Gross-Pitaevskii nonlinear PDE
Electronic Journal of Differential Equations, 2010 A method for finding solutions of the Riccati differential equation $y' = P(x) + Q(x)y + R(x)y^2$ is introduced. Provided that certain relations exist between the coefficient $P(x)$, $Q(x)$ and $R(x)$, the above equation can be solved in closed form.
Anas Al Bastami +2 more
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Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation
Symmetry, Integrability and Geometry: Methods and Applications, 2005 The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method.
Alexey Borisov +2 more
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The Partition Function of the Bose-Einstein Condensation in Parabolic Trap
Makara Seri Sains, 2012 We have discussed the partition function of the Bose-Einstein condensation in parabolic trap associated to the one-dimensional Gross-Pitaevskii equation. The partition function itself is constructed by considering all the energy levels of the macroscopic
Sinta Latifa, Teguh Budi Prayitno
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Derivation of the Time Dependent Gross-Pitaevskii Equation in Two Dimensions. [PDF]
Commun Math Phys, 2019 Jeblick M, Leopold N, Pickl P.
europepmc +1 more source
Tunable band-gap structure and gap solitons in the generalized Gross-Pitaevskii equation with a periodic potential. [PDF]
Sci Rep, 2018 Huang C, Dong L.
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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 Li L, Yu F.
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Macroscopic quantum tunnelling of a Bose-Einstein condensate in a Cubic-Plus-Quadratic Well
AAPPS BulletinWe study the macroscopic quantum tunnelling of an interacting Bose-Einstein condensate in a cubic-plus-quadratic well that was approximately realized in recent experiment.
Rui-Bin Liu +2 more
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AIP AdvancesIn this paper, we study the stability of three-dimensional Bose–Einstein condensates of finite temperatures at which both elastic and inelastic collisions are taken into account.
Rajmohan Sasireka +3 more
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The gravitational bending of acoustic Schwarzschild black hole. [PDF]
Eur Phys J C Part Fields, 2023 Qiao CK, Zhou M.
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Global solutions for 3D nonlocal Gross-Pitaevskii equations with rough data
Electronic Journal of Differential Equations, 2012 We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal interaction potential of Hartree type in three space dimensions. If the potential is even and positive definite or a positive function and its Fourier transform decays ...
Hartmut Pecher
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