Decoupled local/global energy-preserving schemes for the N-coupled nonlinear Schrödinger equations

We develop two local energy-preserving integrators and a global energy-preserving integrator for the general multisymplectic Hamiltonian system. When applied to the 1D and multi-dimensional N-coupled nonlinear Schrödinger equations, the given schemes have the exact preservation of the local/global c...

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Vydáno v:Journal of computational physics Ročník 374; s. 281 - 299
Hlavní autoři: Cai, Jiaxiang, Bai, Chuanzhi, Zhang, Haihui
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge Elsevier Inc 01.12.2018
Elsevier Science Ltd
Témata:
Computation
Computational physics
Discrete gradient method
Energy-preserving algorithm
Fast Fourier transformations
Fourier transforms
Hamiltonian functions
Integrators
Multisymplectic structure
Nonlinear equations
Schrodinger equation
Schrödinger equation
Structure-preserving algorithm
Discrete gradient method
Multisymplectic structure
Energy-preserving algorithm
Structure-preserving algorithm
Schrödinger equation
ISSN:0021-9991, 1090-2716
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Shrnutí:We develop two local energy-preserving integrators and a global energy-preserving integrator for the general multisymplectic Hamiltonian system. When applied to the 1D and multi-dimensional N-coupled nonlinear Schrödinger equations, the given schemes have the exact preservation of the local/global conservation law and are decoupled in the components ψn, n=1,2,…,N, i.e., each of the components can be solved independently. The decoupled feature is significant and helpful for overcoming the computational difficulty of the N-coupled (N≥3) nonlinear Schrödinger equations, especially of the multi-dimensional case. The composition method is employed to improve the accuracy of the schemes in time and the discrete fast Fourier transform is used to reduce the computational complexity. Several numerical experiments are carried out to exhibit the behaviors of the wave solutions. Numerical results confirm the theoretical results.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.07.050