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. T...

and Applied Analysis 3 P(X, Y) = ∑ m i=0 a i (X)Y i is an irreducible polynomial in the complex domain C[X, Y] such that P [X (ξ) , Y (ξ)] = m ∑ i=0 a i (X (ξ)) Y i (ξ) = 0, (13) where a i (X), (i = 0, 1, 2, . . . , m) are polynomials of X and a m (X) ̸ = 0. Equation (13) is called the first integral to (12a) and (12b). Due to the Division Theorem, there exists a polynomial h(X) + g(X)Y in the c...