Intertwining technique for the matrix Schrödinger equation

The intertwining operator technique is applied to the matrix Schrödinger equation. The following related aspects are investigated: the first- and second-order matrix Darboux transformations, factorization, supersymmetry, chains of transformations. An interrelation is established between the differential and integral transformation operators. It is shown that in a particular case the second-order integral transformations turn into ordinary expressions for matrix solutions and potentials obtained by the inverse problem. The method is illustrated by some examples.