Results 81 to 90 of about 2,535 (170)
Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian
, 2017 The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation.
Alessandro Olgiati, Olgiati A.
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Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method
AIP Advances, 2014 We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE) with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of ...
Ying Wang, Yu Zhou
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Physical Review ResearchSolving partial differential equations across multiple length scales represents a formidable challenge where reaching high precision can require a prohibitive amount of computer memory or computing time.
Marcel Niedermeier +4 more
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Partial Differential Equations in Applied MathematicsWe investigate the spatial profiles of periodic localized modes in attractive Bose-Einstein condensates, by solving the mean-field Gross-Pitaevskii equation in the presence of elliptic-type periodic potential.
Nkeh Oma Nfor +2 more
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International Journal of Applied Mathematics and Computer Science, 2019 The present work departs from an extended form of the classical multi-dimensional Gross–Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation.
Hendy Ahmed S., Macías-Díaz Jorge E.
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Quantum Gross-Pitaevskii Equation
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 ...
Verstraete, F +5 more
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Dynamics of Bose-Einstein Condensates Subject to the Pöschl-Teller Potential through Numerical and Variational Solutions of the Gross-Pitaevskii Equation. [PDF]
Materials (Basel), 2020 Pereira LC, Nascimento VAD.
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Stability of the solutions of the Gross-Pitaevskii equation
, 2005 We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties.
Lundh, E +8 more
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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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