In this paper, we consider the robust inverse scattering method for the Ablowitz–Ladik (AL) equation on the non-vanishing background, which can be used to deal with arbitrary-order poles on the branch points and spectral singularities in a unified way. The Darboux matrix is constructed with the aid of loop group method and considered within the framework of robust inverse scattering transform. Various soliton solutions are constructed without using the limit technique. These solutions include general soliton, breathers, as well as high order rogue wave solutions.

中文翻译：

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将 Ablowitz-Ladik 方程聚焦在非消失背景上的鲁棒逆散射方法

在本文中，我们考虑了非消失背景上 Ablowitz-Ladik (AL) 方程的鲁棒逆散射方法，该方法可以统一处理分支点上的任意阶极点和谱奇点。Darboux 矩阵是在循环群方法的帮助下构建的，并在鲁棒逆散射变换的框架内考虑。各种孤子解是在不使用极限技术的情况下构建的。这些解决方案包括一般孤子、呼吸器以及高阶流氓波解决方案。