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Chin. Phys., 2004, Vol. 13(5): 592-597    DOI: 10.1088/1009-1963/13/5/006
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Multi-valued solitary waves in multidimensional soliton systems

Zheng Chun-Longa, Chen Li-Qunb, Zhang Jie-Fangc
a 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; b Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; c Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
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.
Keywords:  multidimensional soliton system      multivalued solitary wave      foldon  
Received:  21 March 2003      Revised:  25 June 2003      Published:  06 July 2005
PACS:  05.45.Yv (Solitons)  
  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
Fund: 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).

Cite this article: 

Zheng Chun-Long, Chen Li-Qun, Zhang Jie-Fang Multi-valued solitary waves in multidimensional soliton systems 2004 Chin. Phys. 13 592

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