Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equation with Trapped Term

Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equation with Trapped Term

Year:    2010

Communications in Computational Physics, Vol. 7 (2010), Iss. 3 : pp. 613–630

Abstract

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrödinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2009.09.057

Communications in Computational Physics, Vol. 7 (2010), Iss. 3 : pp. 613–630

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:   

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  8. Numerical dispersion analysis of a multi-symplectic scheme for the three dimensional Maxwell’s equations

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  9. A New Multi-Symplectic Integration Method for the Nonlinear Schrödinger Equation

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  10. Multisymplectic implicit and explicit methods for Klein—Gordon—Schrödinger equations

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  11. Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

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  12. Local structure-preserving algorithms for the “good” Boussinesq equation

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  13. Derivation of the multisymplectic Crank–Nicolson scheme for the nonlinear Schrödinger equation

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  14. Multisymplectic Scheme for the Improved Boussinesq Equation

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  16. High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations

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  17. A High-Order Conservative Numerical Method for Gross–Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

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  18. LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

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  19. Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrödinger Equation

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  20. Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time

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  22. Multi-symplectic preserving integrator for the Schrödinger equation with wave operator

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  23. Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

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  24. Symplectic structure-preserving integrators for the two-dimensional Gross–Pitaevskii equation for BEC

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