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.
| Published in | American Journal of Physics and Applications (Volume 7, Issue 1) |
| DOI | 10.11648/j.ajpa.20190701.11 |
| Page(s) | 1-7 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Schrödinger Equation, Soliton, Symplectic Algorithm, Optical Communication
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APA Style
Lai Lianyou, Xu Weijian. (2019). Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm. American Journal of Physics and Applications, 7(1), 1-7. https://doi.org/10.11648/j.ajpa.20190701.11
ACS Style
Lai Lianyou; Xu Weijian. Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm. Am. J. Phys. Appl. 2019, 7(1), 1-7. doi: 10.11648/j.ajpa.20190701.11
AMA Style
Lai Lianyou, Xu Weijian. Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm. Am J Phys Appl. 2019;7(1):1-7. doi: 10.11648/j.ajpa.20190701.11
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Download@article{10.11648/j.ajpa.20190701.11,
author = {Lai Lianyou and Xu Weijian},
title = {Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm},
journal = {American Journal of Physics and Applications},
volume = {7},
number = {1},
pages = {1-7},
doi = {10.11648/j.ajpa.20190701.11},
url = {https://doi.org/10.11648/j.ajpa.20190701.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20190701.11},
abstract = {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.},
year = {2019}
}
TY - JOUR T1 - Motion and Interaction of Envelope Solitons in Schrödinger Equation Simulated by Symplectic Algorithm AU - Lai Lianyou AU - Xu Weijian Y1 - 2019/01/21 PY - 2019 N1 - https://doi.org/10.11648/j.ajpa.20190701.11 DO - 10.11648/j.ajpa.20190701.11 T2 - American Journal of Physics and Applications JF - American Journal of Physics and Applications JO - American Journal of Physics and Applications SP - 1 EP - 7 PB - Science Publishing Group SN - 2330-4308 UR - https://doi.org/10.11648/j.ajpa.20190701.11 AB - 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. VL - 7 IS - 1 ER -
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