In this paper, under investigation is a $(2+1)$-dimensional nonlinear ferromagnetic spin chain system with variable coefficients. The system can be used to describe wave propagation in ferromagnetic materials. An algebraic iterative technique is proposed to construct a new hybrid breather and rogue wave solution of the system. Furthermore, abundant interaction behaviours between the breather and rogue wave are observed by choosing variable coefficient function and adjusting the parameters.

中文翻译：

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具有可变系数的 (2 + 1) 维铁磁自旋链系统的混合呼吸和流氓波解决方案

在本文中，正在调查的是$(2+1)$具有可变系数的维非线性铁磁自旋链系统。该系统可用于描述铁磁材料中的波传播。提出了一种代数迭代技术来构造系统的一种新的混合呼吸和流氓波解决方案。此外，通过选择变系数函数和调整参数，观察到呼吸波和流氓波之间丰富的相互作用行为。