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| Numerical solution with symplectic preserving of nonlinear Schrödinger equation |
| Received:June 21, 2014 Revised:August 27, 2014 |
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| DOI：10.7511/jslx201505003 |
| KeyWord:nonlinear Schrödinger equation Hamilton system symplectic preserving energy preserving interval mixed energy |
| Author | Institution |
| 孙雁 |
上海交通大学 船舶海洋与建筑工程学院 工程力学系, 上海 |
| 高强 |
大连理工大学 工业装备结构分析国家重点实验室 工程力学系, 大连 |
| 钟万勰 |
上海交通大学 船舶海洋与建筑工程学院 工程力学系, 上海 ;大连理工大学 工业装备结构分析国家重点实验室 工程力学系, 大连 |
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| Abstract: |
| This paper proposes a new numerical method with symplectic preserving to nonlinear Schrödinger equation,and the validity of this method is proved by numerical examples.We firstly transform nonlinear Schrödinger equation to Hamilton equations and therefore found Hamilton variational principle,followed with the discrete space coordinate through finite element method,precise integration algorithm used on time coordinate,and then with the mixed-energy variational principle,a numerical symplectic-preserving solution of nonlinear Schrödinger equation in the paper is well presented,while energy and mass preserving is realized simultaneously on the integration grids.Numerical examples later on demonstrate the effectiveness of this method. |
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