Of current interest, magneto-optics deals with the phenomena associated with magnetic effects on matter as it emits light, having the potential applications in computer data-storage and waveguides, while ferromagnetic materials are the ones displaying ferromagnetism, such as the various forms of iron, steel, cobalt, nickel, and their alloys. In this paper, in magneto-optics, ferromagnetism, fluid mechanics and plasma physics, we investigate a generalized (3+1)-dimensional variable-coefficient modified Kadomtsev–Petviashvili system for the electromagnetic waves in a ferromagnetic material, or water waves, or dust-acoustic/ion-acoustic/dust–ion-acoustic waves in a plasma. Special cases of the system in those fields are listed out, such as one special case in magneto-optics, which describes the electromagnetic waves in an isotropic charge-free ferromagnetic thin film with the potential application in magneto-optic recording. With symbolic computation, we work out (1) two sets of the variable-coefficient-dependent auto-Bäcklund transformations along with some solitonic features, (2) the variable-coefficient-dependent bilinear forms with the Hirota method and (3) two branches of the variable-coefficient-dependent $N$-soliton solutions with $N$ being a positive integer. Relevant constraints on the variable coefficients are presented.

目前引起人们关注的是，磁光技术处理的是与物质发光相关的磁性现象，在计算机数据存储和波导中具有潜在的应用，而铁磁材料是显示铁磁性的材料，例如各种形式的铁。 ，钢，钴，镍及其合金。在本文中，我们在磁光，铁磁，流体力学和等离子体物理学中研究了广义（3 + 1）维变系数改进的Kadomtsev–Petviashvili系统，用于铁磁材料中的电磁波或水波，或者等离子体中的尘埃声波/离子声波/尘埃离子声波。列出了这些领域中系统的特殊情况，例如磁光中的一种特殊情况，它描述了各向同性的无电荷铁磁薄膜中的电磁波，并潜在地应用于磁光记录。通过符号计算，我们得出（1）两组变量系数相关的自动Bäcklund变换以及一些孤子特征；（2）运用Hirota方法的变量系数相关的双线性形式；（3）两个分支变量系数相关的$ñ$-孤子解决方案 $ñ$是一个正整数。提出了对可变系数的相关约束。