The inverse scattering problem for the two-dimensional nonlinear Klein–Gordon equation Formula: see text is studied. We assume that the unknown nonlinearity Formula: see text of the equation satisfies Formula: see text, Formula: see text (Formula: see text) and Formula: see text (Formula: see text) for any Formula: see text Here, Formula: see text is a positive constant. We establish a reconstruction formula of Formula: see text (Formula: see text) by the knowledge of the scattering operator for the equation. As an application, we also give an expression for higher-order Gâteaux differentials of the scattering operator at 0.
Hironobu Sasaki (Mon,) studied this question.
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