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On inverse scattering for the two-dimensional nonlinear Klein-Gordon equation
The inverse scattering problem for the two-dimensional nonlinear Klein-Gordon equation $u_{tt}-Δu + u = \mathcal{N}(u)$ is studied. We assume that the unknown nonlinearity $\mathcal{N}$ of the equation satisfies $\mathcal{N}\in C^\infty(\mathbb{R};\mathbb{R})$, $\mathcal{N}^{(k)}(y)=O(|y|^{\max\{ 3-
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