Please wait a minute...
Chinese Physics, 2004, Vol. 13(9): 1382-1385    DOI: 10.1088/1009-1963/13/9/002
GENERAL Prev   Next  

Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer-Kaup system

Ma Zheng-Yi (马正义) (马正义)a) †, Zhu Jia-Min (朱加民) (朱加民)a), Zheng Chun-Long (郑春龙)(郑春龙)a)b)
a Department of Physics and Mathematics, Lishui University, Lishui 323000, China; b Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Abstract  This work reveals a novel phenomenon—that the localized coherent structures of a (2﹢1)﹣dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2﹢1)﹣dimensional higher-order Broer-Kaup system as a concrete example. Starting from a Bäcklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.
Keywords:  higher-order Broer-Kaup system      Bäcklund transformation      variable separation approach      Jacobian elliptic function      fractal  
Received:  22 December 2003      Revised:  06 April 2004      Accepted manuscript online: 
PACS:  0340K  
  0365G  
Fund: Project supported by the Foundation of ‘151 Talent Engineering' of Zhengjiang Province, China and by the National Natural Science Foundation of China (Grant No 10172056).

Cite this article: 

Ma Zheng-Yi (马正义), Zhu Jia-Min (朱加民), Zheng Chun-Long (郑春龙) Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer-Kaup system 2004 Chinese Physics 13 1382

[1] Multifractal analysis of the software evolution in software networks
Meili Liu(刘美丽), Xiaogang Qi(齐小刚), and Hao Pan(潘浩). Chin. Phys. B, 2022, 31(3): 030501.
[2] Invariable mobility edge in a quasiperiodic lattice
Tong Liu(刘通), Shujie Cheng(成书杰), Rui Zhang(张锐), Rongrong Ruan(阮榕榕), and Houxun Jiang(姜厚勋). Chin. Phys. B, 2022, 31(2): 027101.
[3] Fractal sorting vector-based least significant bit chaotic permutation for image encryption
Yong-Jin Xian(咸永锦), Xing-Yuan Wang(王兴元), Ying-Qian Zhang(张盈谦), Xiao-Yu Wang(王晓雨), and Xiao-Hui Du(杜晓慧). Chin. Phys. B, 2021, 30(6): 060508.
[4] Fractal microstructure of Ag film via plasma discharge as SERS substrates
Xue-Fen Kan(阚雪芬), Cheng Yin(殷澄), Zhuang-Qi Cao(曹庄琪), Wei Su(苏巍), Ming-Lei Shan(单鸣雷), and Xian-Ping Wang(王贤平). Chin. Phys. B, 2021, 30(12): 125201.
[5] Dynamic crossover in [VIO2+][Tf2N-]2 ionic liquid
Gan Ren(任淦). Chin. Phys. B, 2021, 30(1): 016105.
[6] Analysis of secondary electron emission using the fractal method
Chun-Jiang Bai(白春江), Tian-Cun Hu(胡天存), Yun He(何鋆), Guang-Hui Miao(苗光辉), Rui Wang(王瑞), Na Zhang(张娜), and Wan-Zhao Cui(崔万照). Chin. Phys. B, 2021, 30(1): 017901.
[7] Numerical study on permeability characteristics of fractal porous media
Yongping Huang(黄永平), Feng Yao(姚峰), Bo Zhou(周博), Chengbin Zhang(张程宾). Chin. Phys. B, 2020, 29(5): 054701.
[8] Dynamical response of a neuron-astrocyte coupling system under electromagnetic induction and external stimulation
Zhi-Xuan Yuan(袁治轩), Pei-Hua Feng(冯沛华), Meng-Meng Du(独盟盟), Ying Wu(吴莹). Chin. Phys. B, 2020, 29(3): 030504.
[9] Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms
Yanhui Zhang(张延惠), Xiulan Xu(徐秀兰), Lisha Kang(康丽莎), Xiangji Cai(蔡祥吉), Xu Tang(唐旭). Chin. Phys. B, 2018, 27(5): 053401.
[10] Study on the phase transition of the fractal scale-free networks
Qing-Kuan Meng(孟庆宽), Dong-Tai Feng(冯东太), Yu-Ping Sun(孙玉萍), Ai-Ping Zhou(周爱萍), Yan Sun(孙艳), Shu-Gang Tan(谭树刚), Xu-Tuan Gao(高绪团). Chin. Phys. B, 2018, 27(10): 106402.
[11] Detection of meso-micro scale surface features based on microcanonical multifractal formalism
Yuanyuan Yang(杨媛媛), Wei Chen(陈伟), Tao Xie(谢涛), William Perrie. Chin. Phys. B, 2018, 27(1): 010502.
[12] Polaron effects in cylindrical GaAs/AlxGa1-xAs core-shell nanowires
Hui Sun(孙慧), Bing-Can Liu(刘炳灿), Qiang Tian(田强). Chin. Phys. B, 2017, 26(9): 097302.
[13] Multifractal modeling of the production of concentrated sugar syrup crystal
Sheng Bi(闭胜), Jianbo Gao(高剑波). Chin. Phys. B, 2016, 25(7): 070502.
[14] Electromagnetic backscattering from one-dimensional drifting fractal sea surface II:Electromagnetic backscattering model
Tao Xie(谢涛), William Perrie, Shang-Zhuo Zhao(赵尚卓), He Fang(方贺), Wen-Jin Yu(于文金), Yi-Jun He(何宜军). Chin. Phys. B, 2016, 25(7): 074102.
[15] Exploring the relationship between fractal features and bacterial essential genes
Yong-Ming Yu(余永明), Li-Cai Yang(杨立才), Qian Zhou(周茜), Lu-Lu Zhao(赵璐璐), Zhi-Ping Liu(刘治平). Chin. Phys. B, 2016, 25(6): 060503.
No Suggested Reading articles found!