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.