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Inverse fixed angle scattering and backscattering for a nonlinear Schrödinger equation in 2D

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  • We investigate two inverse scattering problems for the nonlinear Schrödinger equation $$ -\Delta u(x) + h(x,|u(x)|)u(x) = k^{2}u(x), \quad x \in \mathbb{R}^2, $$ where $h$ is a very general and possibly singular combination of potentials. The method of Born approximation is applied for the recovery of local singularities and jumps from fixed angle scattering and backscattering data.
    Mathematics Subject Classification: 35P25, 35R30.


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