Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation

DOI10.1016/j.cnsns.2017.05.024OpenAlexW2563402977MaRDI QIDQ2204827

Pangiotis G. Kevrekidis, Efstathios G. Charalampidis, Patrick E. Farrell

Publication date: 16 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.08145

zbMATH Keywords

Bose-Einstein condensationGross-Pitaevskii equationstability and bifurcation analysisdeflated continuation

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX) Partial differential equations (35-XX)

Related Items (14)

Constrained high-index saddle dynamics for the solution landscape with equality constraints ⋮ Exploring critical points of energy landscapes: from low-dimensional examples to phase field crystal PDEs ⋮ Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization ⋮ Nonextensive Gross Pitaevskii Equation ⋮ Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices ⋮ Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation ⋮ A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross--Pitaevskii Equation ⋮ Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data ⋮ On the characterization of vortex configurations in the steady rotating Bose–Einstein condensates ⋮ Perturbation theory for Bose–Einstein condensates on bounded space domains ⋮ Automatic Exploration Techniques of Numerical Bifurcation Diagrams Illustrated by the Ginzburg--Landau Equation ⋮ Computing Multiple Solutions of Topology Optimization Problems ⋮ Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction ⋮ Control of Bifurcation Structures using Shape Optimization

Uses Software

• FEniCS

Cites Work

• Unnamed Item
• Emergent nonlinear phenomena in Bose-Einstein condensates. Theory and experiment
• Nonlinear modes of a macroscopic quantum oscillator
• Global bifurcation of vortex and dipole solutions in Bose-Einstein condensates
• Spectral and dynamical stability of nonlinear waves
• Rotating matter waves in Bose-Einstein condensates
• The Defocusing Nonlinear Schrödinger Equation
• Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
• Excited states in the large density limit: a variational approach
• Multipoles and vortex multiplets in multidimensional media with inhomogeneous defocusing nonlinearity
• Spectral Stability of Vortices in Two-Dimensional Bose–Einstein Condensates via the Evans Function and Krein Signature
• Nonlinear modes for the Gross–Pitaevskii equation—a demonstrative computation approach

This page was built for publication: Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation