Results 111 to 120 of about 33,314 (234)

Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco, Yanghong Huang, Zeng Liu, Vitaly Moroz   +3 more
wiley   +1 more source

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

Ricerche di Matematica, 2018
Bäcklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of Bäcklund 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. Examples and explicit solutions of the Gross-
Carillo, Sandra, Zullo, Federico
openaire   +3 more sources

Optical Soliton Structure Solutions, Sensitivity, and Modulation Stability Analysis in the Chiral Nonlinear Schrödinger Equation With Bohm Potential

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This study examines the optical soliton structure solutions, sensitivity, and modulation stability analysis of the chiral nonlinear Schrödinger equation (NLSE) with Bohm potential, a basic model in nonlinear optics and quantum mechanics. The equation represents wave group dynamics in numerous physical systems, involving quantum Hall and nonlinear ...
Ishrat Bibi, Shah Muhammad, Muhammad Shakeel, Baboucarr Ceesay, Ivan Giorgio   +4 more
wiley   +1 more source

On nonlocal Gross-Pitaevskii equations with periodic potentials [PDF]

Journal of Mathematical Physics, 2012
The Gross-Pitaevskii equation is a widely used model in physics, in particular in the context of Bose-Einstein condensates. However, it only takes into account local interactions between particles. This paper demonstrates the validity of using a nonlocal formulation as a generalization of the local model.
openaire   +3 more sources

Using Artificial Neural Networks to Solve the Gross–Pitaevskii Equation

Axioms
The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials.
Ioannis G. Tsoulos, Vasileios N. Stavrou, Dimitrios Tsalikakis   +2 more
doaj   +1 more source

Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity

, 2006
We study defect modes of a Bose-Einstein condensate in an optical lattice with a localized defect within the framework of the one-dimensional Gross-Pitaevskii equation.
A. I. Anselm, V. V. Konotop, Valeriy A. Brazhnyi, Vladimir V. Konotop, Víctor M. Pérez-García   +4 more
core   +1 more source

Exploring Solitons and Modulation Instability in the Nonlinear Fractional Coupled Painlevé–Burgers Model

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This work reveals the novel types of exact solitons for the coupled (2 + 1)‐dimensional Painlevé’s–Burgers model in the sense of novel fractional derivative. To gain the different kinds of exact solitons, we utilized the modified extended direct algebraic technique.
Waseem Razzaq, Asim Zafar, Naif Almusallam, Fawaz Khaled Alarfaj, Pramita Mishra   +4 more
wiley   +1 more source

Dynamics characterization of modified Gross–Pitaevskii equation

Physica A: Statistical Mechanics and its Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Filho, Victo S., Machado, Birajara S., Francisco, Gerson, Tomio, Lauro   +3 more
openaire   +2 more sources

Slowly rotating Bose Einstein condensate galactic dark matter halos, and their rotation curves

European Physical Journal C: Particles and Fields, 2018
If dark matter is composed of massive bosons, a Bose–Einstein condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction.
Xiaoyue Zhang, Man Ho Chan, Tiberiu Harko, Shi-Dong Liang, Chun Sing Leung   +4 more
doaj   +1 more source

Coupling Dynamics and Linear Polarization Phenomena in Codirectional Polariton Waveguide Couplers

Advanced Optical Materials, Volume 12, Issue 33, November 25, 2024.
Rozas and co‐workers examine integrated devices utilizing polariton waveguides, forming codirectional couplers. With appropriate parameters, the transfer of polariton condensates between the arms is triggered and tunable Josephson‐type oscillations arise.
Elena Rozas, Alexey Yulin, Sebastian Klembt, Sven Höfling, María Dolores Martín, Luis Viña   +5 more
wiley   +1 more source