Abstract
In this paper the nonstationary scattering problems for the hyperbolic system on the whole plane and on the half-plane in the case of two incident waves with the same velocity are considered. The scattering operators for the hyperbolic system on the whole plane and on the half-plane are defined and by using the Gelfand–Levitan–Marchenko (GLM) method the uniqueness of the recovery of the potential from the scattering operators is proved. Moreover, a nonlinear evolution equation in 2 + 1 dimensions which can be integrated by the inverse scattering transform method is presented in association with the considered scattering problems.
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