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(2+1)维非线性Schrodinger型方程的同宿轨道

沈守枫 张隽

沈守枫, 张隽. (2+1)维非线性Schrodinger型方程的同宿轨道[J]. 应用数学和力学, 2008, 29(10): 1254-1260.
引用本文: 沈守枫, 张隽. (2+1)维非线性Schrodinger型方程的同宿轨道[J]. 应用数学和力学, 2008, 29(10): 1254-1260.
SHEN Shou-feng, ZHANG Jun. Homoclinic Orbits for Some (2+1)-Dimensional Nonlinear SchrLdinger-Like Equations[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1254-1260.
Citation: SHEN Shou-feng, ZHANG Jun. Homoclinic Orbits for Some (2+1)-Dimensional Nonlinear SchrLdinger-Like Equations[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1254-1260.

(2+1)维非线性Schrodinger型方程的同宿轨道

基金项目: 国家自然科学基金资助项目(10501040)
详细信息
    作者简介:

    沈守枫(1977- ),男,浙江天台人,副教授,博士(联系人.E-mail:mathssf@yahoo.com.cn).

  • 中图分类号: O175

Homoclinic Orbits for Some (2+1)-Dimensional Nonlinear SchrLdinger-Like Equations

  • 摘要: 研究了几类(2+1)维非线性Schrdinger型方程同宿轨道的问题.利用Hirota双线性算子方法,通过给出的相关变换, 得到了包括(2+1)维的长短波相互作用方程, 广义Zakharov方程,Mel'nikov方程和g-Schrdinger方程的同宿轨道解的显式解析表达式,从而讨论了这些方程的同宿轨道.
  • [1] Herbst B M,Ablowitz M J.Numerically induced chaos in the nonlinear Schrdinger equation[J].Physical Review Letters,1989,62(18):2065-2068. doi: 10.1103/PhysRevLett.62.2065
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    [3] Hirota R.Direct methods in soliton theory[A].In:Bullough R K,Caudey E J,Eds.Solitons[C].Berlin:Springer,1980,157-176.
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    [5] Herbst B M,Ablowitz M J,Ryan E.Numerical homoclinic instabilities and the complex modified Korteweg-de Vries Equation[J].Computer Physics Communications,1991,65(1):137-142. doi: 10.1016/0010-4655(91)90165-H
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    [8] 张隽,郭柏灵,沈守枫.Davey-Stewartson方程的同宿轨道[J].应用数学和力学,2005,26(2):127-129.
    [9] ZHANG Jun,GUO Bo-ling,SHEN Shou-feng.Homoclinic orbits of the doubly periodic Davey-Stewartson equation[J].Progress in Natural Science,2004,14(11):1031-1032. doi: 10.1080/10020070412331344761
    [10] Derek W C Lai,Kwok W Chow.‘Positon’ and ‘Dromion’solutions of the (2+1) dimensional long wave-short wave resonance interaction equations[J].Journal of the Physical Society of Japan,1999,68(6):1847-1853. doi: 10.1143/JPSJ.68.1847
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    [12] Radha R,Lakshmanan M.Localized coherent structures and integrability in a generalized (2+1)-dimensional nonlinear Schrdinger equation[J].Chaos, Solitons and Fractals,1997,8(1):17-25. doi: 10.1016/S0960-0779(96)00090-2
    [13] Mel'nikov V K.Reflection of waves in nonlinear integrable systems[J].Journal of Mathematical Physics,1987,28(2):2603-2609. doi: 10.1063/1.527752
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出版历程
  • 收稿日期:  2008-05-07
  • 修回日期:  2008-09-05
  • 刊出日期:  2008-10-15

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