中国物理B ›› 1995, Vol. 4 ›› Issue (6): 401-405.doi: 10.1088/1004-423X/4/6/001

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NEW SYMMETRIES AND LIE ALGEBRAS OF THE GENERAL KdV EQUATION

张解放   

  1. Institute of Nonlinear Physics and Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:1994-08-02 出版日期:1995-06-20 发布日期:1995-06-20

NEW SYMMETRIES AND LIE ALGEBRAS OF THE GENERAL KdV EQUATION

ZHANG JIE-FANG (张解放)   

  1. Institute of Nonlinear Physics and Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:1994-08-02 Online:1995-06-20 Published:1995-06-20

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摘要： The strong symmetry of the general KdV equation is factorized to a simple form and then the inverse strong symmetry is obtained explicitly. Acting a strong symmetry of the general KdV equation on the trivial symmetry and the known re symmetry, we obtain four new sets of symmetries of the general KdV equation. All these sets of symmetries constitute an infinite dimensional Lie algebra.

Abstract: The strong symmetry of the general KdV equation is factorized to a simple form and then the inverse strong symmetry is obtained explicitly. Acting a strong symmetry of the general KdV equation on the trivial symmetry and the known $\tau_{\rm c}$ symmetry, we obtain four new sets of symmetries of the general KdV equation. All these sets of symmetries constitute an infinite dimensional Lie algebra.

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations) 02.30.Rz (Integral equations) 02.10.Ud (Linear algebra) 11.30.-j (Symmetry and conservation laws)