Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation

DOI10.1016/j.cnsns.2020.105255zbMath1453.37070arXiv1912.00023OpenAlexW3011524864MaRDI QIDQ2208074

Yanyan Li

Publication date: 23 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/1912.00023

zbMATH Keywords

bifurcationsspectral stability analysisdeflated continuation

Mathematics Subject Classification ID

Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Bifurcations in context of PDEs (35B32) Computational methods for bifurcation problems in dynamical systems (37M20) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

Related Items (8)

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 ⋮ A finite element toolbox for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates ⋮ Nonextensive Gross Pitaevskii Equation ⋮ Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients ⋮ A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the Gross--Pitaevskii Equation ⋮ Numerical bifurcation and stability for the capillary-gravity Whitham equation ⋮ Control of Bifurcation Structures using Shape Optimization

Uses Software

• AUTO
• AUTO-86
• FEniCS

Cites Work

• Automated solution of differential equations by the finite element method. The FEniCS book
• Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation
• Bose-Einstein Condensation and Superfluidity
• Feast Eigensolver for Non-Hermitian Problems
• FEAST As A Subspace Iteration Eigensolver Accelerated By Approximate Spectral Projection
• Combining Deflation and Nested Iteration for Computing Multiple Solutions of Nonlinear Variational Problems
• Numerical Methods for Large Eigenvalue Problems
• The Defocusing Nonlinear Schrödinger Equation
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
• Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
• Classification of Solitary Wave Bifurcations in Generalized Nonlinear Schrödinger Equations
• DYNAMICS OF BRIGHT MATTER WAVE SOLITONS IN A BOSE–EINSTEIN CONDENSATE
• VORTICES IN BOSE–EINSTEIN CONDENSATES: SOME RECENT DEVELOPMENTS
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