We investigate the inverse scattering problem of the perturbed biharmonic operator by studying the recovery process of the magnetic field $ {\mathbf{A}} $ and the potential field $ V $. We show that the high-frequency asymptotic of the scattering amplitude of the biharmonic operator uniquely determines $ {\rm{curl}}\ {\mathbf{A}} $ and $ V-\frac{1}{2}\nabla\cdot{\mathbf{A}} $. We study the near-field scattering problem and show that the high-frequency asymptotic expansion up to an error $ \mathcal{O}(\lambda^{-4}) $ recovers above two quantities with no additional information about $ {\mathbf{A}} $ and $ V $. We also establish stability estimates for $ {\rm{curl}}\ {\mathbf{A}} $ and $ V-\frac{1}{2}\nabla\cdot{\mathbf{A}} $.

中文翻译：

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双谐波算子的反散射和稳定性

通过研究磁场$ {\ mathbf {A}} $和势场$ V $的恢复过程，我们研究了扰动双谐波算子的逆散射问题。我们表明，双谐波算子的散射幅度的高频渐近唯一地确定了$ {\ rm {curl}} \ {\ mathbf {A}} $和$ V- \ frac {1} {2} \ nabla \ cdot {\ mathbf {A}} $。我们研究了近场散射问题，并表明直到误差$ \ mathcal {O}（\ lambda ^ {-4}）$的高频渐近展开都恢复了两个以上的量，而没有关于$ {\ mathbf的附加信息{A}} $和$ V $。我们还为$ {\ rm {curl}} \ {\ mathbf {A}} $和$ V- \ frac {1} {2} \ nabla \ cdot {\ mathbf {A}} $建立稳定性估计。