Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm
American Journal of Physics and Applications
Volume 7, Issue 1, January 2019, Pages: 1-7
Received: Nov. 18, 2018;
Accepted: Dec. 14, 2018;
Published: Jan. 21, 2019
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Lai Lianyou, College of Information Engineering, Jimei University, Xiamen, China; College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, China
Xu Weijian, College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, China
The expression of Gaussian envelope soliton in Schrödinger equations are given and proved in this paper. According to the characteristics of the Gauss envelope soliton, further proposed that the interaction between Gaussian envelope solitons exists in Schrödinger equation. The symplectic algorithm for solving Schrödinger equation is proposed after analysis characteristics of Schrödinger equation. First, the Schrödinger equation is transformed into the standard Hamiltonian canonical equation by separating the real and imaginary parts of wave function. Secondly, the symplectic algorithm is implemented by using the Euler center difference method for the canonical equation. The conserved quantity of symplectic algorithm is given, and the stability of symplectic algorithm is proved. The numerical simulation experiment was carried out on Schrödinger equation in Gauss envelope soliton motion and multi solitons interaction. The experimental results show that the proposed method is correct and the symplectic algorithm is effective.
Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm, American Journal of Physics and Applications.
Vol. 7, No. 1,
2019, pp. 1-7.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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