Invariant Manifolds of Traveling Waves of the 3D Gross–Pitaevskii Equation in the Energy Space
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-018-3189-6
Abstract: We study the local dynamics near general unstable traveling waves of the 3D Gross–Pitaevskii equation in the energy space by constructing smooth local invariant center-stable, center-unstable and center manifolds. We also prove that (i) the… read more here.
Keywords: pitaevskii equation; waves gross; traveling waves; center ... See more keywords
Search for an Analytical Solution in the Three-Dimensional Gross–Pitaevskii Equation
Sign Up to like & getrecommendations! Published in 2017 at "Computational Mathematics and Modeling"
DOI: 10.1007/s10598-017-9359-0
Abstract: The Gross–Pitaevskii equation is at the core of the mathematical problem of the propagation of a Bose–Einstein condensate (BEC). In this article, we look for an analytical soliton solution in the three-dimensional Gross–Pitaevskii equation. We… read more here.
Keywords: pitaevskii equation; solution; solution three; analytical solution ... See more keywords
Bose–Einstein condensation under the cubic–quintic Gross–Pitaevskii equation in radial domains
Sign Up to like & getrecommendations! Published in 2018 at "Annals of Physics"
DOI: 10.1016/j.aop.2017.11.009
Abstract: Abstract We study stationary and quasi-stationary solutions for the cubic–quintic Gross–Pitaevskii equation modeling Bose–Einstein condensates (BECs) in one, two, and three spatial dimensions under the assumption of radial symmetry with the BEC dynamics influenced by… read more here.
Keywords: pitaevskii equation; cubic quintic; quintic gross; gross pitaevskii ... See more keywords
Periodic, complexiton solutions and stability for a (2+1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation
Sign Up to like & getrecommendations! Published in 2018 at "Physica B: Condensed Matter"
DOI: 10.1016/j.physb.2018.03.042
Abstract: Abstract This paper presents an investigation of a (2 + 1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation. Periodic and complexiton solutions are obtained. Solitons solutions are also gotten through the periodic solutions. Numerical solutions via the… read more here.
Keywords: pitaevskii equation; coefficient gross; equation bose; dimensional variable ... See more keywords
Effective self-similar expansion for the Gross-Pitaevskii equation
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review A"
DOI: 10.1103/physreva.97.043604
Abstract: We consider an effective scaling approach for the free expansion of a one-dimensional quantum wave packet, consisting in a self-similar evolution to be satisfied on average, i.e. by integrating over the coordinates. A direct comparison… read more here.
Keywords: pitaevskii equation; self similar; gross pitaevskii; expansion ... See more keywords
Rogue waves of the dissipative Gross–Pitaevskii equation with distributed coefficients
Sign Up to like & getrecommendations! Published in 2020 at "European Physical Journal Plus"
DOI: 10.1140/epjp/s13360-020-00651-x
Abstract: By introducing a suitable ansatz and employing the similarity transformation technique, we construct the first- and second-order rational solutions for a quasi-one-dimensional (1D) dissipative Gross–Pitaevskii (GP) equation with a time-varying cubic nonlinearity and an external… read more here.
Keywords: pitaevskii equation; rogue waves; rogue; dissipative gross ... See more keywords
Soliton Solutions and Collisions for the Multicomponent Gross–Pitaevskii Equation in Spinor Bose–Einstein Condensates
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Problems in Engineering"
DOI: 10.1155/2020/4632434
Abstract: In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain… read more here.
Keywords: pitaevskii equation; bose einstein; soliton solutions; gross pitaevskii ... See more keywords
A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space–Fractional Gross–Pitaevskii Equation
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Applied Mathematics and Computer Science"
DOI: 10.2478/amcs-2019-0053
Abstract: Abstract 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. It is… read more here.
Keywords: pitaevskii equation; space; conservative scheme; gross pitaevskii ... See more keywords