Results 21 to 30 of about 32,263 (260)

The inverse problem for the Gross - Pitaevskii equation [PDF]

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2010
Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first method, suggested by the work by Kondrat'ev and Miller (1966), applies to one-dimensional (1D) GPE. It
Boris A. Malomed, Fallani L., Kivshar Y. S., Kondrat’ev I. G., Kondrat’ev I. G., Pitaevskii L. P., Yury A. Stepanyants   +6 more
core   +7 more sources

Formal analytical solutions for the Gross-Pitaevskii equation [PDF]

Physica D: Nonlinear Phenomena, 2007
Considering the Gross-Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter $\Phi (x)$ and for the chemical potential $\mu $ as a function of a unique dimensionless non-linear parameter $\Lambda $.
Abdullaev, Alfimov, Anderson, Bao, Baym, Bender, Bradley, Bradley, Burger, C. Trallero-Giner, Dalfovo, Davis, Edwards, Eiermann, Esslinger, Gradshteyn, Gross, Han, Hau, Hyouguchi, Joseph L. Birman, Julio C. Drake-Perez, Khaykovich, Kivshar, Kivshar, Konotop, Lord, Mikhlin, Mikhlin, Morse, Myatt, Petrovskii, Pitaevskii, Pitaevskii, Ponomarev, Pu, Pérez-García, Pérez-García, Ruprecht, Salasnich, Salasnich, Strecker, Trallero-Giner, V. López-Richard, Witthaut, Yang, Yukalov, Yukalov   +47 more
core   +2 more sources

Quantum fluctuations of many-body dynamics around the Gross–Pitaevskii equation [PDF]

Annales de l'Institut Henri Poincare. Analyse non linéar, 2023
We consider the evolution of a gas of $N$ bosons in the three-dimensional Gross-Pitaevskii regime (in which particles are initially trapped in a volume of order one and interact through a repulsive potential with scattering length of the order $1/N$). We
Cristina Caraci, Jakob Oldenburg, B. Schlein   +2 more
semanticscholar   +1 more source

Approximation of a two‐dimensional Gross–Pitaevskii equation with a periodic potential in the tight‐binding limit

Mathematische Nachrichten, Volume 297, Issue 10, Page 3870-3886, October 2024.
Abstract The Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the x$x$‐direction and a harmonic oscillator potential in the y$y$‐direction in the so‐called tight‐binding limit.
Steffen Gilg, Guido Schneider
openalex   +2 more sources

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 ...
Stephen J. Gustafson, Kenji Nakanishi, Tai‐Peng Tsai   +2 more
openalex   +3 more sources

Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation [PDF]

IMA Journal of Numerical Analysis, 2022
In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation.
Christian Döding, P. Henning
semanticscholar   +1 more source

The Gross-Pitaevskii equation: Bäcklund transformations and admitted solutions [PDF]

Ricerche di Matematica, 2018
B cklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of B cklund transformations admitted by this equation are constructed. Schwartzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation.
Sandra Carillo, Federico Zullo
openalex   +5 more sources

Variational approach to multimode nonlinear optical fibers. [PDF]

Nanophotonics
Abstract We analyze the spatiotemporal solitary waves of a graded‐index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schrödinger equation approach, we derive an effective one‐dimensional Lagrangian associated with the Laguerre–Gauss modes with a generic radial mode number p and azimuthal index m.
Lorenzi F, Salasnich L.
europepmc   +2 more sources

Orbital frontiers: harnessing higher modes in photonic simulators. [PDF]

Nanophotonics
Abstract Photonic platforms have emerged as versatile and powerful classical simulators of quantum dynamics, providing clean, controllable optical analogs of extended structured (i.e., crystalline) electronic systems. While most realizations to date have used only the fundamental mode at each site, recent advances in structured light – particularly the
Noh J, Schulz J, Benalcazar W, Jörg C.
europepmc   +2 more sources

Superconvergence of time invariants for the Gross-Pitaevskii equation [PDF]

Mathematics of Computation, 2020
This paper considers the numerical treatment of the time-dependent Gross-Pitaevskii equation. In order to conserve the time invariants of the equation as accurately as possible, we propose a Crank-Nicolson-type time discretization that is combined with a
P. Henning, Johan Wärnegård
semanticscholar   +1 more source