中国物理B ›› 2004, Vol. 13 ›› Issue (9): 1382-1385.doi: 10.1088/1009-1963/13/9/002

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

马正义1, 朱加民1, 郑春龙2   

  1. (1)Department of Physics and Mathematics, Lishui University, Lishui 323000, China; (2)Department of Physics and Mathematics, Lishui University, Lishui 323000, China; Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2003-12-22 修回日期:2004-04-06 出版日期:2004-06-21 发布日期:2005-06-21
  • 基金资助:
    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).

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)   

  1. a Department of Physics and Mathematics, Lishui University, Lishui 323000, China; b Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2003-12-22 Revised:2004-04-06 Online:2004-06-21 Published:2005-06-21
  • Supported by:
    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).

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摘要： 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 B?cklund 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.

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.

Key words: higher-order Broer－Kaup system, Bäcklund transformation, variable separation approach, Jacobian elliptic function, fractal

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