ON THE TRANSFORMATIONS OF THE POTENTIALS,INTEGRABLE EVOLUTION EQUATIONS AND B（A¨）CKLUND TRANSFORMATIONS

摘要

＜正＞ The generalization of the AKNS method,Calogero method and Konopelchenkomethod is given in three respects,First,the new fundamental relations associated with thematrix spectral problem and a new explicit expression related to the matrixes B and Cwhich are contained in the transformations of the transition matrixes are obtained.Thenthe wide classes of the integrable evolution equations are conveniently derived withoutimproperly assuming B=C.Finally,an important property of the operator LA is showed,the conditions connected with the temporal half of the B（a|¨）cklund transformations and thenew simple expressions of the integrals of motion are deduced.