Abstract:
The solvability of two-dimensional inverse scattering problems for the Klein–Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier–Stokes equation is solvable.
Key words:acoustic, Klein–Gordon, Schrödinger, Riccati, Navier–Stokes, Gelfand–Levitan, and Volterra equations, Dirac system, solvability of inverse scattering problems.
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