中国物理B ›› 2004, Vol. 13 ›› Issue (5): 592-597.doi: 10.1088/1009-1963/13/5/006

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Multi-valued solitary waves in multidimensional soliton systems

郑春龙1, 陈立群2, 张解放3   

  1. (1)Department of Physics, Zhejiang Lishui Normal College, Lishui 323000, China; Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; (2)Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (3)Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:2003-03-21 修回日期:2003-06-25 出版日期:2004-05-06 发布日期:2005-07-06
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10172056) and by the Foundation of Zhejiang Lishui Normal College (Grant Nos KZ03009 and KZ03005).

Multi-valued solitary waves in multidimensional soliton systems

Zheng Chun-Long (郑春龙)abc, Chen Li-Qun (陈立群)b, Zhang Jie-Fang (张解放)bc   

  1. a Department of Physics, Zhejiang Lishui Normal College, Lishui 323000, Chinab Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chinac Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2003-03-21 Revised:2003-06-25 Online:2004-05-06 Published:2005-07-06
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10172056) and by the Foundation of Zhejiang Lishui Normal College (Grant Nos KZ03009 and KZ03005).

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摘要： Considering that folded phenomena are rather universal in nature and some arbitrary functions can be included in the exact excitations of many (2+1)-dimensional soliton systems, we use adequate multivalued functions to construct folded solitary structures in multi-dimensions. Based on some interesting variable separation results in the literature, a common formula with arbitrary functions has been derived for suitable physical quantities of some significant (2+1)-dimensional soliton systems like the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) model, the generalized Nizhnik－Novikov－Veselov (GNNV) system and the new (2+1)-dimensional long dispersive wave (NLDW) system. Then a new special type of two-dimensional solitary wave structure, i.e. the folded solitary wave and foldon, is obtained. The novel structure exhibits interesting features not found in the single valued solitary excitations.

关键词: multidimensional soliton system, multivalued solitary wave, foldon

Abstract: Considering that folded phenomena are rather universal in nature and some arbitrary functions can be included in the exact excitations of many (2+1)-dimensional soliton systems, we use adequate multivalued functions to construct folded solitary structures in multi-dimensions. Based on some interesting variable separation results in the literature, a common formula with arbitrary functions has been derived for suitable physical quantities of some significant (2+1)-dimensional soliton systems like the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) model, the generalized Nizhnik－Novikov－Veselov (GNNV) system and the new (2+1)-dimensional long dispersive wave (NLDW) system. Then a new special type of two-dimensional solitary wave structure, i.e. the folded solitary wave and foldon, is obtained. The novel structure exhibits interesting features not found in the single valued solitary excitations.

Key words: multidimensional soliton system, multivalued solitary wave, foldon

中图分类号:  (Solitons)

  • 05.45.Yv
03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)