Abstract: Let us consider
the system of differential equations given on a half-axis
where
’s are complex-valued functions satisfying and
(e
and c are constants)
For the above
system of equations, given boundary conditions and solution
together with asymptotic expression considered matrix function on
the half-axis, subsquare matrices obtained from this function and scattering
data by means of their inverses are defined.
Relationships
between scattering matrix and scattering data are determined when the problem is
given on the whole axis and coefficients are zero in case of By using analytic representation of
the solution it is shown that the coefficient of the system of equations is
defined uniquely under the solvability condition of Riemann problem.
Keywords and phrases: inverse scattering, scattering data, Riemann problem.
