Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients

doi:10.1088/1674-1056/25/1/010205

Abstract In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.

Keywords: multi-symplectic form formulas variational integrators conservation laws nonlinear Schrödinger equations

Received: 08 July 2015
Revised: 18 September 2015
Accepted manuscript online:

PACS:	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Bf	(Finite-difference methods)
	45.10.Na	(Geometrical and tensorial methods)
	47.10.Df	(Hamiltonian formulations)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11401259) and the Fundamental Research Funds for the Central Universities, China (Grant No. JUSRR11407).

Corresponding Authors: Cui-Cui Liao
E-mail: cliao@jiangnan.edu.cn

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Cui-Cui Liao(廖翠萃), Jin-Chao Cui(崔金超), Jiu-Zhen Liang(梁久祯), Xiao-Hua Ding(丁效华) Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients 2016 Chin. Phys. B 25 010205

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Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients

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