On the transformations of the potentials, integrable evolution equations and Bäcklund transformations (Q1819295)

A generalization of the AKNS method, Calogero method and Konopilchenko method is given in three directions. First, new fundamental relations associated with the matrix special problem and a new explicit expression related to the matrices B and C which are contained in the transformations of the transition matrices are obtained. Then the wide class of integrable evolution equations are conveniently derived without improperly assuming \(B=C\). Finally, an important property of the operator \(L_ A\) is shown, the conditions connected with the temporal half of the Bäcklund transformations and the new simple expressions of the integrals of motion are deduced.