中国物理B ›› 2007, Vol. 16 ›› Issue (6): 1505-1509.doi: 10.1088/1009-1963/16/6/002

• GENERAL • 上一篇    下一篇

Pfaffianization of the variable-coefficient Kadomtsev--Petviashvili equation

张晴帆, 范恩贵   

  1. Department of Mathematics, Fudan University, Shanghai 200433, China
  • 收稿日期:2006-10-25 修回日期:2006-12-11 出版日期:2007-06-20 发布日期:2007-06-20
  • 基金资助:
    Project supported by the National Key Basic Research Project of China (2004CB318000), the National Science Foundation of China (Grant No~10371023) and Shanghai Shuguang Project of China (Grant No~02SG02).

Pfaffianization of the variable-coefficient Kadomtsev--Petviashvili equation

Zhang Qing-Fan(张晴帆)† and Fan En-Gui(范恩贵)   

  1. Department of Mathematics, Fudan University, Shanghai 200433, China
  • Received:2006-10-25 Revised:2006-12-11 Online:2007-06-20 Published:2007-06-20
  • Supported by:
    Project supported by the National Key Basic Research Project of China (2004CB318000), the National Science Foundation of China (Grant No~10371023) and Shanghai Shuguang Project of China (Grant No~02SG02).

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摘要： This paper constructs more general exact solutions than $N$-soliton solution and Wronskian solution for variable-coefficient Kadomtsev--Petviashvili (KP) equation. By using the Hirota method and Pfaffian technique, it finds the Grammian determinant-type solution for the variable-coefficient KP equation (VCKP), the Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions for the Pfaffianized VCKP equation.

Abstract: This paper constructs more general exact solutions than $N$-soliton solution and Wronskian solution for variable-coefficient Kadomtsev--Petviashvili (KP) equation. By using the Hirota method and Pfaffian technique, it finds the Grammian determinant-type solution for the variable-coefficient KP equation (VCKP), the Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions for the Pfaffianized VCKP equation.

Key words: variable-coefficient KP equation, Pfaffian technique, Pfaffian solution

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations)