Matrix solutions of the equations BU_t= -U_xx + 2U^3+B [U_x,U]+4cU: development of the method of the inverse problem of dissipation - Siroid , I.-P. P. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Complex solution matrices of the nonlinear Schrödinger equation BUt = -U_xx+2U^3+B[U_x, U]+4cU are found and the method of the inverse scattering problem is subjected to a natural extension. That is, for the nonself-conjugate L — А Lax doublet that arises for this equation, the presence of chains of adjoint vectors for the operator L is taken into account by means the corresponding normed chains. A uniqueness theorem for the Cauchy problem for the above Schrödinger equation is obtained. Here B=pmatrix 0 & 1 -1 & 0pmatrix, [M, N] = MN — NM, and c is a parameter.