Results 31 to 40 of about 634 (180)
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
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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Optimal Bilinear Control of Gross--Pitaevskii Equations [PDF]
SIAM Journal on Control and Optimization, 2013 A mathematical framework for optimal bilinear control of nonlinear Schrödinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects.
Michael Hintermüller +3 more
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Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons
SciPost Physics, 2022 Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a ...
Jakub Kopyciński, Maciej Łebek, Maciej Marciniak, Rafał Ołdziejewski, Wojciech Górecki, Krzysztof Pawłowski
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Logarithmic Gross-Pitaevskii equation
Communications in Partial Differential Equations, 2023 We consider the Schr{ö}dinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the energy space for the standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions.
Carles, Rémi, Ferriere, Guillaume
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Scattering for the Gross-Pitaevskii equation [PDF]
Mathematical Research Letters, 2006 We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic ...
Gustafson, S. +2 more
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The Gross–Pitaevskii equation and Bose–Einstein condensates [PDF]
European Journal of Physics, 2013 The Gross-Pitaevskii equation is discussed at the level of an advanced course on statistical physics. In the standard literature the Gross-Pitaevskii equation is usually obtained in the framework of the second quantisation formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses.
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Formal analytical solutions for the Gross–Pitaevskii equation [PDF]
Physica D: Nonlinear Phenomena, 2008 8 ...
Trallero-Giner, C. +3 more
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Multiple front and pulse solutions in spatially periodic systems
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
wiley +1 more source
Polaron Dynamics in a Quasi-Two-Dimensional Bose–Einstein Condensate
Universe, 2023 The concept of polaron quasiparticles was first introduced in the pioneering papers by Landau and Feynman in the 1930s and 1940s. It describes the phenomenon of an external particle producing a bound state in an embedded medium.
Shukhrat N. Mardonov +3 more
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Deriving the Gross-Pitaevskii equation [PDF]
Mathematical Results in Quantum Mechanics, 2014 5 pages; contribution to the proceedings of ...
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