Spin waves, the collective excitations of the electron spin systems in the ferromagnetic metals, are used in the telecommunication systems and radars. Under investigation is a (2+1)-dimensional nonlinear Schrödinger equation which describes the spin dynamics of a Heisenberg ferromagnetic spin chain. We construct its Lax pair which is different from the published ones. With respect to the coherent magnetism amplitude for the bosonic operators at the spin lattice sites, we derive the n-th-order breather solutions with n as a positive integer. We convert, under certain conversion conditions, the breathers to the lumps, rogue waves and two types of periodic waves which are named as the periodic-I and periodic-II waves in this paper. The breathers and periodic-I waves are affected by the uniaxial crystal field anisotropy parameter A as well as the bilinear exchange interactions. Periods of the periodic-II waves are affected by A and the lattice parameter. Via the second-order breather solutions, interactions of the two breathers, of the two periodic waves and of a breather and a periodic-I wave are graphically discussed. Through the theoretical and graphical analyses, it is found that the lumps and rogue waves are the long-wave limits of the breathers and periodic waves, respectively.

自旋波是铁磁金属中电子自旋系统的集体激发，用于电信系统和雷达。正在研究的是一个 (2+1) 维非线性薛定谔方程，它描述了海森堡铁磁自旋链的自旋动力学。我们构建了它的 Lax 对，它与已发布的不同。关于自旋晶格位置玻色子算子的相干磁振幅，我们推导出n阶呼吸器解，其中n作为正整数。在一定的转换条件下，我们将呼吸波转换为团块、杂乱波和两种类型的周期波，本文将其称为周期I波和周期II波。呼吸器和周期 I 波受单轴晶体场各向异性参数A以及双线性交换相互作用的影响。周期 II 波的周期受A和晶格参数的影响。通过二阶呼吸器解，两个呼吸器、两个周期波以及一个呼吸器和一个周期 I 波的相互作用被图形化地讨论。通过理论和图解分析发现，团块波和流氓波分别是呼吸波和周期波的长波极限。