中国物理B ›› 2003, Vol. 12 ›› Issue (1): 11-16.doi: 10.1088/1009-1963/12/1/302

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Exact solution and exotic coherent soliton structures of the (2+1)-dimensional generalized nonlinear Schrodinger equation

郑春龙1, 黄文华2, 盛正茂3, 张解放4   

  1. (1)Department of Physics, Lishui Normal College, Lishui 323000, China; (2)Department of Physics, Yichun University, Yichun 336000, China; (3)Department of Physics, Zhejiang University, Hangzhou 310027, China; (4)Institute of Nonlinear Physics, Zhejiang Normal University,Jinhua 321004, China
  • 收稿日期:2002-06-02 修回日期:2002-07-30 出版日期:2003-01-20 发布日期:2003-01-20
  • 基金资助:
    Project supported by the Foundation of "151 Talent Engineering" of Zhejiang Province, China, and the Natural Science Foundation of Zhejiang Province, China (Grant No 100039)

Exact solution and exotic coherent soliton structures of the (2+1)-dimensional generalized nonlinear Schrödinger equation

Zheng Chun-Long (郑春龙)abc, Zhang Jie-Fang (张解放)bd,  Sheng Zheng-Mao (盛正茂)c, Huang Wen-Hua (黄文华)bce   

  1. a Department of Physics, Lishui Normal College, Lishui 323000, China; b  Institute of Nonlinear Physics, Zhejiang Normal University,Jinhua 321004, China; c Department of Physics, Zhejiang University, Hangzhou 310027, China; d Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; e Department of Physics, Yichun University, Yichun 336000, China
  • Received:2002-06-02 Revised:2002-07-30 Online:2003-01-20 Published:2003-01-20
  • Supported by:
    Project supported by the Foundation of "151 Talent Engineering" of Zhejiang Province, China, and the Natural Science Foundation of Zhejiang Province, China (Grant No 100039)

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摘要： In this paper, a variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized nonlinear Schrodinger equation:$\i\varphi_t-(\alpha \beta)\varphi_{xx}+(\alpha+\beta)\varphi_{yy}-2\lambda \varphi \bigg[(\alpha+\beta)\bigg(\dint_{-\infty}^x|\varphi|_{y}^2\dd x+u_1(y,t)\bigg) $$-(\alpha-\beta)\bigg(\dint_{-\infty}^y|\varphi|_{x}^2\ddy+u_2(x,t)\bigg)\bigg]=0.$ By applying a special B\"{a}cklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, breathers and instantons are constructed.

Abstract: In this paper, a variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized nonlinear Schrodinger equation:${\rm i}\varphi_t-(\alpha \beta)\varphi_{xx}+(\alpha+\beta)\varphi_{yy}-2\lambda \varphi \bigg[(\alpha+\beta)\bigg(\int_{-\infty}^x|\varphi|_{y}^2{\rm d} x+u_1(y,t)\bigg) $$-(\alpha-\beta)\bigg(\int_{-\infty}^y|\varphi|_{x}^2{\rm d}y+u_2(x,t)\bigg)\bigg]=0.$ By applying a special B?cklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, breathers and instantons are constructed.

Key words: variable separation approach, generalized nonlinear Schr?dinger equation, coherent structure

中图分类号:  (Solitons)

  • 05.45.Yv
03.65.Ge (Solutions of wave equations: bound states) 03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 02.30.-f (Function theory, analysis)