中国物理B ›› 1999, Vol. 8 ›› Issue (4): 241-251.doi: 10.1088/1004-423X/8/4/001

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SYMMETRIES AND DROMION SOLUTION OF A (2+1)-DIMENSIONAL NONLINEAR SOHR?DINGER EQUATION

陈一新1, 阮航宇2   

  1. (1)Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China; (2)Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China; Institute of Modern Physics, Normal College of Ningbo University, Ningbo 315211, China
  • 收稿日期:1997-11-26 修回日期:1998-11-16 出版日期:1999-04-15 发布日期:1999-04-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. 196003).

SYMMETRIES AND DROMION SOLUTION OF A (2+1)-DIMENSIONAL NONLINEAR SOHR?DINGER EQUATION

Ruan Hang-yu (阮航宇)a, Chen Yi-xin (陈一新)b   

  1. a Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China; b Institute of Modern Physics, Normal College of Ningbo University, Ningbo 315211, China
  • Received:1997-11-26 Revised:1998-11-16 Online:1999-04-15 Published:1999-04-20
  • Supported by:
    Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. 196003).

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摘要： The Painlevé property, infinitely many symmetries and exact solutions of a (2+1)-dimensional nonlinear Schr?dinger equation, which are obtained from the constraints of the Kadomtsev-Petviashvili equation, are studied in this paper. The Painlevé property is proved by the Weiss-Kruskal approach, the infinitely many symmetries are obtained by the formal series symmetry method and the dromion-like solution which is localized exponentially in all directions is obtained by a variable separation method.

Abstract: The Painlevé property, infinitely many symmetries and exact solutions of a (2+1)-dimensional nonlinear Schr$\ddot{o}$dinger equation, which are obtained from the constraints of the Kadomtsev-Petviashvili equation, are studied in this paper. The Painlevé property is proved by the Weiss-Kruskal approach, the infinitely many symmetries are obtained by the formal series symmetry method and the dromion-like solution which is localized exponentially in all directions is obtained by a variable separation method.

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations) 02.30.Ik (Integrable systems)