B?cklund变换与n孤子解

B?cklund Transformations and n Soliton Solutions

中文关键词:  KdV方程  sine-Gordon方程  B?cklund变换  Hirota方法  Wronski行列式

英文关键词:KdV equation  sine-Gordon equation  B?cklund tansformation  Hirota method  Wronskian determinant.

中文摘要:

      本文首先证明了KdV方程与sine-Gordon方程不同形式的B?cklund变换是相互等价的;其次从双线性导数形式的B?cklund变换出发给出多孤子解的Hirota表示与Wronski行列式表示,并利用Vandermonde行列式说明这两种孤子解的表示是一致的.

英文摘要:

      Different B?cklund transformations for KdV and sine-Gordon equations are proved to be equivalent and the soliton solution is derived by Hirota method and Wronskian technique. The uniformity of the solutions is shown.