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Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System

Part of:Infinite-dimensional Hamiltonian systemsEquations of mathematical physics and other areas of applicationApproximation methods and numerical treatment of dynamical systems

Published online by Cambridge University Press:  28 November 2017

Hao Fu,
Weien Zhou,
Xu Qian and
Songhe Song
Xu Qian*
Affiliation:
Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan 410072, China
Songhe Song
Affiliation:
Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan 410072, ChinaState Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha, Hunan 410073, China
*
*Corresponding author. Email:qianxu@nudt.edu.cn (X. Qian)

Abstract

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This paper introduces two novel conformal structure-preserving algorithms for solving the coupled damped nonlinear Schrödinger (CDNLS) system, which are based on the conformal multi-symplectic Hamiltonian formulation and its conformal conservation laws. The proposed algorithms can preserve corresponding conformal multi-symplectic conservation law and conformal momentum conservation law in any local time-space region, respectively. Moreover, it is further shown that the algorithms admit the conformal charge conservation law, and exactly preserve the dissipation rate of charge under appropriate boundary conditions. Numerical experiments are presented to demonstrate the conformal properties and effectiveness of the proposed algorithms during long-time numerical simulations and validate the analysis.

Keywords

Conformal conservation lawsconformal structure-preserving algorithmscoupled damped nonlinear Schrödinger systemdissipation rate of charge

MSC classification

Secondary:35Q55: NLS-like equations (nonlinear Schrödinger)37K05: Hamiltonian structures, symmetries, variational principles, conservation laws37M15: Symplectic integrators

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017, pp. 1383 - 1403
Copyright
Copyright © Global-Science Press 2017 

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