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Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays |
| Li-Yuan Ma(马立媛)1, Jia-Liang Ji(季佳梁)2, Zong-Wei Xu(徐宗玮)3, Zuo-Nong Zhu(朱佐农)3 |
1 Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China;
2 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
3 School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China |
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Abstract We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.
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Received: 24 August 2017
Revised: 25 December 2017
Accepted manuscript online:
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PACS:
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02.30.Ik
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(Integrable systems)
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05.45.Yv
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(Solitons)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964). |
Corresponding Authors:
Zuo-Nong Zhu
E-mail: znzhu@sjtu.edu.cn
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Cite this article:
Li-Yuan Ma(马立媛), Jia-Liang Ji(季佳梁), Zong-Wei Xu(徐宗玮), Zuo-Nong Zhu(朱佐农) Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays 2018 Chin. Phys. B 27 030201
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