Results 21 to 30 of about 15,069 (140)

Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori

Mathematics in Engineering, 2023
In this paper we consider traveling waves for the Gross-Pitaevskii equation which are $ T $-periodic in each variable. We prove that if $ T $ is large enough, there exists a solution as a global minimizer of the corresponding action functional.
Francisco Javier Martínez Sánchez , David Ruiz   +1 more
doaj   +1 more source

Dirac exciton-polariton condensates in photonic crystal gratings. [PDF]

Nanophotonics
Abstract Bound states in the continuum have recently been utilized in photonic crystal gratings to achieve strong coupling and ultralow threshold condensation of exciton–polariton quasiparticles with atypical Dirac‐like features in their dispersion relation.
Sigurðsson H, Nguyen HC, Nguyen HS.
europepmc   +2 more sources

Instability of standing waves for the inhomogeneous Gross-Pitaevskii equation

AIMS Mathematics, 2020
In this paper, we consider the instability of standing waves for an inhomogeneous Gross-Pitaevskii equation \[ i\psi_t +\Delta \psi -a^2|x|^2\psi +|x|^{-b}|\psi|^{p}\psi=0. \] This equation arises in the description of nonlinear waves such as propagation
Yongbin Wang, Binhua Feng
doaj   +1 more source

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.
A. Knowles, L. Erdős, L. Erdős, N. Benedikter, P. Pickl   +4 more
core   +1 more source

Integrability of the Gross-Pitaevskii Equation with Feshbach Resonance management

, 2008
In this paper we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential.
Abdullaev, Abdullaev, Ablowitz, Ablowitz, Anderson, Belmonte-Beitia, Blow, Brazhnyi, Chen, Chen, Dalfovo, Dun Zhao, Gardner, Gross, Hong-Gang Luo, Hua-Yue Chai, Kevrekidis, Konotop, Konotop, Konotop, Liang, Mihanache, Novikov, Pelinovsky, Perez-Garcia, Pitaevskii, Roberts, Sakaguchi, Satsuma, Serkin, Serkin, Serkin, Stenger, Tenorio, Weiss, Yuce, Zabusky, Zakharov, Zakharov, Zhao   +39 more
core   +1 more source

Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping

International Journal of Differential Equations, 2013
We study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping.
Renato Colucci, Gerardo R. Chacón, Andrés Vargas   +2 more
doaj   +1 more source

Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on $\mathbb {T}^{4}$

Forum of Mathematics, Pi, 2022
We consider the $\mathbb {T}^{4}$ cubic nonlinear Schrödinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross–Pitaevskii hierarchy, an uncommon method for NLS analysis which is ...
Xuwen Chen, Justin Holmer
doaj   +1 more source

Bright soliton behaviour of the integer and fractional nonlinear Gross-Pitaevskii equation having the generalized cubic-quintic nonlinearities via the polytropic approximation

Journal of Taibah University for Science
Based on the generalized model of the cubic-quintic Gross-Pitaevskii equation with polytropic approximation, we novelly utilize an F-expansion method to identify bright soliton dynamics of systems modelled by the cubic-quintic Gross-Pitaevskii with ...
Qingru Wang, Ying Wang, Xiaogang Tang, Changmin Hu   +3 more
doaj   +1 more source

Remarks on the Blow-Up Solutions for the Critical Gross-Pitaevskii Equation

Abstract and Applied Analysis, 2013
This paper is concerned with the blow-up solutions of the critical Gross-Pitaevskii equation, which models the Bose-Einstein condensate. The existence and qualitative properties of the minimal blow-up solutions are obtained.
Xiaoguang Li, Chong Lai
doaj   +1 more source

Comparison of finite‐difference schemes for the Gross‐Pitaevskii equation

Mathematical Modelling and Analysis, 2009
A conservative finite‐difference scheme for numerical solution of the Gross‐Pitaevskii equation is proposed. The scheme preserves three invariants of the problem: the L 2 norm of the solution, the impulse functional, and the energy functional.
Vyacheslav A. Trofimov, Nikolai Peskov
doaj   +1 more source