  Inverse scattering problem for the operator representing sum of the operator
of the third derivative on semi-axis and of the operator of multiplication by a
real function is studied in this paper. Properties of Jost solutions of such an
operator are studied and it is shown that these Jost solutions are solutions of
the Riemann boundary value problem on a system of rays. The main system of
linear singular integral equations is derived. This system is equivalent to the
solution of inverse scattering problem.
