∂̄-Method with nonzero background potential. Application to inverse scattering for the two-dimensional acoustic equation

We generalize a number of formulas of the ∂̄-method for the Schrödinger equation to the case of nonzero background potential. As a corollary we have found the following reciprocity property of the Faddeev function h: h(k, l) = h(-l, -k), k, l ∈ ℂⁿ, k² = l², Im k = Im l ≠ 0, where h is a non-analytic extension of the scattering amplitude to the complex domain. As an application we prove the uniqueness theorem and give a reconstruction procedure in the inverse scattering problem for the two-dimensional acoustic equation.