中国物理B ›› 2006, Vol. 15 ›› Issue (1): 45-52.doi: 10.1088/1009-1963/15/1/008

• GENERAL • 上一篇    下一篇

Two classes of fractal structures for the (2+1)-dimensional dispersive long wave equation

马正义, 郑春龙   

  1. College of Science, Zhejiang Lishui University, Lishui 323000, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2004-08-16 修回日期:2005-06-17 出版日期:2006-01-20 发布日期:2006-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272071), the Natural Science Foundation of Zhejiang Province, China (Grant No Y604106) and the Key Academic Discipline of Zhejiang Province, China (Grant No 200412).

Two classes of fractal structures for the (2+1)-dimensional dispersive long wave equation

Ma Zheng-Yi (马正义), Zheng Chun-Long (郑春龙)   

  1. College of Science, Zhejiang Lishui University, Lishui 323000, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2004-08-16 Revised:2005-06-17 Online:2006-01-20 Published:2006-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272071), the Natural Science Foundation of Zhejiang Province, China (Grant No Y604106) and the Key Academic Discipline of Zhejiang Province, China (Grant No 200412).

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摘要： Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.

Abstract: Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.

Key words: mapping approach, DLW equation, explicit solution, fractal

中图分类号:  (Fractals)

  • 05.45.Df
05.45.Yv (Solitons)