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Uniqueness in the inverse scattering problem for Hartree type equation. (English) Zbl 0999.35095

Summary: We consider the inverse scattering problem for the following Hartree type equation: \[ i\;\frac{\partial u}{\partial t}=-\Delta u+(|x|^{-\sigma}*|u|^2)u. \] We prove uniqueness for the inverse scattering problem with respect to the power \(\sigma\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs
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