数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (4): 426-437.

• 论文 • 上一篇    下一篇

FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRÖDINGER EICENVALUE PROBLEM

黄烈德, 夏忠奂   

  1. Tongiji University, Shanghai 200092, China
  • 收稿日期:1992-07-11 修回日期:1993-09-23 出版日期:1994-12-25 发布日期:1994-12-25

FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRÖDINGER EICENVALUE PROBLEM

Huang Liede, Xia Zhonghuan   

  1. Tongiji University, Shanghai 200092, China
  • Received:1992-07-11 Revised:1993-09-23 Online:1994-12-25 Published:1994-12-25

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摘要： The explicit solution of a large class of nonlinear evolution equations associated with the isospectral Schröding equation is given in terms of the Fedholm determinant of a family of linear integral operators,whose kernels solve the corresponding base equations. Using Fredholm theory,the relation between the Fredholm determinant method and the inverse scattering method is clarified. Moreover,it is also shown that the Cauchy problems for these nonlinear evolution equations can be solved by the Fredholm determinant method.

Abstract: The explicit solution of a large class of nonlinear evolution equations associated with the isospectral Schröding equation is given in terms of the Fedholm determinant of a family of linear integral operators,whose kernels solve the corresponding base equations. Using Fredholm theory,the relation between the Fredholm determinant method and the inverse scattering method is clarified. Moreover,it is also shown that the Cauchy problems for these nonlinear evolution equations can be solved by the Fredholm determinant method.

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