Solitonic Combinations, Commuting Nonselfadjoint Operators, and Applications

In this paper, we consider applications of the connection between soliton theory and commuting nonselfadjoint operator theory, established by Livšic Avishai. An approach to inverse scattering problem wave equations is presented, based on colligation (or vessel theory) in case bounded operators a Hilbert space, when one belongs larger class nondissipative with asymptotics corresponding curves. The generalized Gelfand–Levitan–Marchenko equation cases different differential (the Korteweg–de Vries equation, Schrödinger Sine–Gordon Davey–Stewartson equation) are derived. Relations input output open systems, obtained. these two cases, Sturm–Liouville 3-dimensional equation), satisfied components