A hyperplane-constrained continuation method for near singularity in coupled nonlinear Schrödinger equations

DOI10.1016/j.apnum.2009.11.007zbMath1190.65161OpenAlexW2043753029MaRDI QIDQ973086

Wen-Wei Lin, Yueh-Cheng Kuo, Shih-Feng Shieh, Wei-Chung Wang

Publication date: 28 May 2010

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: http://ntur.lib.ntu.edu.tw/bitstream/246246/216368/1/902.pdf

zbMATH Keywords

stabilityfinite difference methodnumerical examplesnonlinear opticsnumerical solutionscoupled nonlinear Schrödinger equationsbifurcation analysishyperplane-constrained continuation methodnearly singular systemsprimal stalk solutions

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite difference methods for boundary value problems involving PDEs (65N06) Bifurcations in context of PDEs (35B32)

Related Items (4)

Tracking local optimality for cost parameterized optimization problems ⋮ Exploring bistability in rotating Bose-Einstein condensates by a quotient transformation invariant continuation method ⋮ Exploring ground states and excited states of spin-1 Bose-Einstein condensates by continuation methods ⋮ Rotational quotient procedure: a tracking control continuation method for PDEs on radially symmetric domains

Uses Software

• svdpack

Cites Work

• Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate
• A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations
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• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Bifurcation analysis of a two-component Bose-Einstein condensate
• A continuation BSOR-Lanczos--Galerkin method for positive bound states of a multi-component Bose-Einstein condensate
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• Deflation Techniques and Block-Elimination Algorithms for Solving Bordered Singular Systems
• Stable Solvers and Block Elimination for Bordered Systems
• Mixed block elimination for linear systems with wider borders
• Solitary waves andNcoupled nonlinear equations
• Special set and solutions of coupled nonlinear schr dinger equations
• Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
• Ground States and Dynamics of Multicomponent Bose--Einstein Condensates
• Numerical Methods for Bifurcations of Dynamical Equilibria
• Liapunov–Schmidt Reduction and Continuation for Nonlinear Schrödinger Equations
• Periodic solutions for a system of four coupled nonlinear Schrödinger equations

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