A Fast Time Splitting Finite Difference Approach to Gross–Pitaevskii Equations

DOI10.4208/cicp.OA-2020-0131zbMath1473.65096OpenAlexW3136828957MaRDI QIDQ5163228

Marco Caliari, Simone Zuccher

Publication date: 3 November 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cicp.oa-2020-0131

zbMATH Keywords

unbounded domainnonlinear Schrödinger equationvortex ringsdark structuresfast matrix exponentialGross-Pitaevskii boundary conditions

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (4)

Creation of quantum knots and links driven by minimal surfaces ⋮ Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrödinger Equation ⋮ Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type ⋮ Symmetric-conjugate splitting methods for evolution equations of parabolic type

Uses Software

• GSGPEs
• INFFTM
• NLSEmagic

Cites Work

• Unnamed Item
• A primer on quantum fluids
• GSGPEs: a MATLAB code for computing the ground state of systems of Gross-Pitaevskii equations
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• INFFTM: fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
• Dynamics of thin vortex rings
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Vortex Rings
• Padé approximations of solitary wave solutions of the Gross–Pitaevskii equation
• A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and Its Application to the Nonlinear Schrödinger Equation
• The Dynamics and Interaction of Quantized Vortices in the Ginzburg–Landau–Schrödinger Equation
• Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation
• Reliability of the time splitting Fourier method for singular solutions in quantum fluids

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