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

作　　者：黄烈德 夏忠奂 

出　　处：《Acta Mathematica Scientia》1994年第4期426-437,共12页数学物理学报（B辑英文版）

摘　　要：The explicit solution of a large class of nonlinear evolution equations associated with the isospectral Schroding 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.The explicit solution of a large class of nonlinear evolution equations associated with the isospectral Schroding 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.

分 类 号：O175[理学—数学]