Volume 9, Issue 6
Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System

Hao Fu, Weien Zhou, Xu Qian & Songhe Song

Adv. Appl. Math. Mech., 9 (2017), pp. 1383-1403.

Published online: 2017-09

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  • Abstract

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 laws, conformal structure-preserving algorithms, coupled damped nonlinear Schrödinger system, dissipation rate of charge.

  • AMS Subject Headings

35Q55, 37K05, 37M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1383, author = {}, title = {Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {1383--1403}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0164}, url = {http://global-sci.org/intro/article_detail/aamm/10184.html} }
TY - JOUR T1 - Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1383 EP - 1403 PY - 2017 DA - 2017/09 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0164 UR - https://global-sci.org/intro/article_detail/aamm/10184.html KW - Conformal conservation laws, conformal structure-preserving algorithms, coupled damped nonlinear Schrödinger system, dissipation rate of charge. AB -

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.

Hao Fu, Weien Zhou, Xu Qian & Songhe Song. (2020). Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System. Advances in Applied Mathematics and Mechanics. 9 (6). 1383-1403. doi:10.4208/aamm.OA-2016-0164
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