Non-linearity arising from mutual interactions is one of the two main difficulties to be addressed in inverse scattering. In this paper, we first review and describe under a common rationale some approaches which have been introduced in literature in order to counteract non-linearity. In particular, we focus on possible rewritings of the Lippman Schwinger basic equation such to reduce the ‘degree of non-linearity’ of inverse scattering problem. In detail, three different rewritings are discussed and compared by emphasizing similarities and differences, and in the same ‘rewriting’ spirit, we also summarize and discuss the ‘Virtual Experiments’ framework. Then, some possible and effective joint exploitations of the above concepts are introduced, discussed and tested against numerical examples.

中文翻译：

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定量非线性逆散射：通过智能重写基本方程式的可能性

相互作用引起的非线性是逆散射中要解决的两个主要困难之一。在本文中，我们首先以一个共同的原理回顾并描述了一些文献中为抵消非线性而引入的方法。尤其是，我们着重研究Lippman Schwinger基本方程的可能重写，以减少逆散射问题的“非线性程度”。详细地，通过强调相同点和不同点来讨论和比较三种不同的重写，并且以相同的“重写”精神，我们还总结和讨论了“虚拟实验”框架。然后，对上述概念进行了一些可能和有效的联合开发，并针对数值示例进行了测试。