中国物理B ›› 2006, Vol. 15 ›› Issue (11): 2500-2505.doi: 10.1088/1009-1963/15/11/006

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The pth-order periodic solutions for a family of N-coupled nonlinear SchrOdingerequations

刘官厅   

  1. College of Mathematics Science, Inner Mongolia Normal University,Huhhot010022, China
  • 收稿日期:2006-03-03 修回日期:2006-06-18 出版日期:2006-11-20 发布日期:2006-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10461006).

The pth-order periodic solutions for a family of N-coupled nonlinear SchrOdingerequations

Liu Guan-Ting(刘官厅)†   

  1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China
  • Received:2006-03-03 Revised:2006-06-18 Online:2006-11-20 Published:2006-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10461006).

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摘要： By using the solutions of an auxiliary Lam\'e equation, a direct algebraic method is proposed to construct the exact solutions of $N$-coupled nonlinear Schr\"{o}dinger equations. The abundant higher-order exact periodic solutions of a family of $N$-coupled nonlinear Schr\"{o}dinger equations are explicitly obtained with the aid of symbolic computation and they include corresponding envelope solitary and shock wave solutions.

关键词: Lam\'e equation, $N$-coupled nonlinear Schr?dinger equations, higher-order periodic solution, symbolic computation

Abstract: By using the solutions of an auxiliary Lam\'e equation, a direct algebraic method is proposed to construct the exact solutions of $N$-coupled nonlinear Schr?dinger equations. The abundant higher-order exact periodic solutions of a family of $N$-coupled nonlinear Schr?dinger equations are explicitly obtained with the aid of symbolic computation and they include corresponding envelope solitary and shock wave solutions.

Key words: Lam\'e equation, $N$-coupled nonlinear Schr\"{o}dinger equations, higher-order periodic solution, symbolic computation

中图分类号:  (Partial differential equations)

  • 02.30.Jr
42.81.Dp (Propagation, scattering, and losses; solitons)