Two-dimensional inverse scattering for quasi-linear biharmonic operator

<p style='text-indent:20px;'>The subject of this work concerns the classical direct and inverse scattering problems for quasi-linear perturbations two-dimensional biharmonic operator. The first zero order might be complex-valued singular. We show existence solutions to problem in Sobolev space <inline-formula><tex-math id="M1">\begin{document}$ W^1_{\infty}( \mathbb{{R}}^2) $\end{document}</tex-math></inline-formula>. Then can formulated as follows: does knowledge far field pattern uniquely determine unknown coefficients given differential operator? It turns out that answer question is affirmative Moreover, we present a numerical method reconstruction coefficients, which from practical point view thought recovery fixed energy measurements.</p>