Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

doi:10.1088/1674-1056/27/3/030201

中国物理B ›› 2018, Vol. 27 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/27/3/030201

• GENERAL • 下一篇

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

Li-Yuan Ma(马立媛), Jia-Liang Ji(季佳梁), Zong-Wei Xu(徐宗玮), Zuo-Nong Zhu(朱佐农)

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

收稿日期:2017-08-24 修回日期:2017-12-25 出版日期:2018-03-05 发布日期:2018-03-05
通讯作者: Zuo-Nong Zhu E-mail:znzhu@sjtu.edu.cn
基金资助:
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).

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

Received:2017-08-24 Revised:2017-12-25 Online:2018-03-05 Published:2018-03-05
Contact: Zuo-Nong Zhu E-mail:znzhu@sjtu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: nonintegrable dNLS equation, solitary waves, chaos, nonlinear nearest-neighbor interaction

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.

Key words: nonintegrable dNLS equation, solitary waves, chaos, nonlinear nearest-neighbor interaction

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons)

马立媛, 季佳梁, 徐宗玮, 朱佐农. Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays[J]. 中国物理B, 2018, 27(3): 30201-030201.

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[J]. Chin. Phys. B, 2018, 27(3): 30201-030201.

参考文献 24

[1]	Scott A C and Macneil L 1983 Phys. Lett. A 98 87
[2]	Sievers A J and Takeno S 1988 Phys. Rev. Lett. 61 970
[3]	Marquii P, Bilbault J M and Remoissenet M 1995 Phys. Rev. E 51 6127
[4]	Davydov A S 1973 J. Theor. Biol. 38 559
[5]	Cai D, Bishop A R and Gronbech-Jensen N 1994 Phys. Rev. Lett. 72 591
[6]	Eisenberg H, Silberberg Y, Morandotti R, Boyd A and Aitchison J 1998 Phys. Rev. Lett. 81 3383
[7]	Morandotti R, Peschel U, Aitchison J, Eisenberg H and Silberberg Y 1999 Phys. Rev. Lett. 83 2726
[8]	Christodoulides D N and Joseph R J 1988 Opt. Lett. 13 794
[9]	Gómez-Gardeñes J and Floría L M 2004 Chaos 14 1130
[10]	Pando L C L and Doedel E J 2004 Phys. Rev. E 69 036603
[11]	Pando L C L and Doedel E J 2005 Phys. Rev. E 71 056201
[12]	Pando L C L and Doedel E J 2007 Phys. Rev. E 75 016213
[13]	Pando L C L and Doedel E J 2009 Physica D 238 687
[14]	Ablowitz M J, Musslimani Z H and Biondini G 2002 Phys. Rev. E 65 026602
[15]	Öster M, Johansson M and Eriksson A 2003 Phys. Rev. E 67 056606
[16]	Rojas-Rojas S, Vicencio R A, Molina M I and Abdullaev F Kh 2011 Phys. Rev. A 84 033621
[17]	Yang J 2010 Nonlinear Waves in Integrable and Nonintegrable Systems (Society for Industrial and Applied Mathematics, Philadelphia) pp. 163-168, 359-366
[18]	Petviashvili V I 1976 Sov. J. Plasma Phys. 2 257
[19]	Ablowitz M J and Biondini G 1998 Opt. Lett. 23 1668
[20]	Pelinovsky D E and Stepanyants Y A 2004 SIAM J. Numer. Anal. 42 1110
[21]	Flach S and Willis C R 1998 Phys. Rep. 295 181
[22]	Flach S and Gorbach A V 2008 Phys. Rep. 467 1
[23]	Eilbeck J C, Lomdahl P S and Scott A C 1985 Physica D 16 318
[24]	Herbst B M and Ablowitz M J 1989 Phys. Rev. Lett. 62 2065

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 24

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. 中国物理B, 2023, 32(3): 30203-030203.
[2]	Chunlei Fan(范春雷) and Qun Ding(丁群). A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain[J]. 中国物理B, 2023, 32(1): 10501-010501.
[3]	Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability[J]. 中国物理B, 2023, 32(1): 10507-010507.
[4]	Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map[J]. 中国物理B, 2022, 31(8): 80504-080504.
[5]	Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback[J]. 中国物理B, 2022, 31(7): 74205-074205.
[6]	Wenjie Yang(杨文杰). Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation[J]. 中国物理B, 2022, 31(2): 20201-020201.
[7]	Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network[J]. 中国物理B, 2022, 31(2): 20502-020502.
[8]	Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Energy spreading, equipartition, and chaos in lattices with non-central forces[J]. 中国物理B, 2022, 31(2): 20506-020506.
[9]	Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Resonance and antiresonance characteristics in linearly delayed Maryland model[J]. 中国物理B, 2022, 31(12): 120502-120502.
[10]	Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree[J]. 中国物理B, 2022, 31(11): 110503-110503.
[11]	Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system[J]. 中国物理B, 2022, 31(1): 10501-010501.
[12]	You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Control of chaos in Frenkel-Kontorova model using reinforcement learning[J]. 中国物理B, 2021, 30(5): 50503-050503.
[13]	Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵). Dynamics analysis in a tumor-immune system with chemotherapy[J]. 中国物理B, 2021, 30(5): 58201-058201.
[14]	Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷). Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation[J]. 中国物理B, 2021, 30(12): 120502-120502.
[15]	Fang Yuan(袁方), Cheng-Jun Bai(柏承君), and Yu-Xia Li(李玉霞). Cascade discrete memristive maps for enhancing chaos[J]. 中国物理B, 2021, 30(12): 120514-120514.