中国物理B ›› 2003, Vol. 12 ›› Issue (5): 472-478.doi: 10.1088/1009-1963/12/5/302

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Solitons in a generalized (2+1)-dimensional Ablowitz－Kaup－Newell－Segur system

郑春龙1, 盛正卯2, 吴锋民3, 陈立群4, 张解放5   

  1. (1)Department of Physics, Lishui Normal College, Lishui 323000, China; Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Physics, Zhejiang University, Hangzhou 310027, China; (2)Department of Physics, Zhejiang University, Hangzhou 310027, China; (3)Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; (4)Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (5)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:2002-10-21 修回日期:2003-01-15 出版日期:2003-05-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the Foundation of "151 Talent Engineering" of Zhejiang Province, China, the National Basic Research Foundation for Nonlinear Science of China, and the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

Solitons in a generalized (2+1)-dimensional Ablowitz－Kaup－Newell－Segur system

Zheng Chun-Long (郑春龙)abc, Zhang Jie-Fang (张解放)bd, Wu Feng-Min (吴锋民)d, Sheng Zheng-Mao (盛正卯)c, Chen Li-Qun (陈立群)b    

  1. a Department of Physics, Lishui Normal College, Lishui 323000, Chinab Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chinac Department of Physics, Zhejiang University, Hangzhou 310027, China; d Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2002-10-21 Revised:2003-01-15 Online:2003-05-16 Published:2005-03-16
  • Supported by:
    Project supported by the Foundation of "151 Talent Engineering" of Zhejiang Province, China, the National Basic Research Foundation for Nonlinear Science of China, and the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

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摘要： In the previous Letter (Zheng C L and Zhang J F 2002 Chin. Phys. Lett. 19 1399), a localized excitation of the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps, rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations, which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.

Abstract: In the previous Letter (Zheng C L and Zhang J F 2002 Chin. Phys. Lett. 19 1399), a localized excitation of the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps, rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations, which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.

Key words: GAKNS system, variable separation approach, soliton

中图分类号:  (Solitons)

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