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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Two remarks on solutions of Gross-Pitaevskii equations on Zhidkov spaces [PDF]
, 2006 Olivier Goubet
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A Reduced Order Modeling technique to study bifurcating phenomena:\n application to the Gross-Pitaevskii equation [PDF]
, 2019 Federico Pichi +2 more
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The Cauchy problem for the Gross–Pitaevskii equation
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2006 We prove global wellposedness of the two-dimensional and three-dimensional Gross–Pitaevskii equations in the natural energy space. Résumé On établit que le problème de Cauchy pour l'équation de Gross–Pitaevskii est bien posé dans l'espace d'énergie naturel, en dimensions deux et trois.
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Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation [PDF]
, 2023 Riccardo Molle +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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Density matrix form of Gross-Pitaevskii equation
, 2014 We consider the generalized pure state density matrix which depends on different time moments. The evolution equation for this density matrix is obtained in case where the density matrix corresponds to the solutions of Gross-Pitaevskii equation.
Chernega, V. N. +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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C programs for solving the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap [PDF]
, 2012 D. Vudragović +4 more
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Numerical Simulations for the Gross-Pitaevskii Equation
, 2023 T.-Y. Na, Urinov SX
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