Magnetooptic Studies on a Ferromagnetic Material via an Extended (3+1)-Dimensional Variable-Coefficient Modified Kadomtsev-Petviashvili System

In this paper, we symbolically compute an extended (3+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system for the electromagnetic waves in a certain ferromagnetic material, ion-acoustic/dust-ion-acoustic/dust-acoustic waves in a sort of plasma, or water waves. Particular instances of the system in magnetooptics, ferromagnetism, plasma mechanics and fluid dynamics are presented, such as one case in magnetooptics, describing the electromagnetic waves in a ferromagnetic thin charge-free isotropic film with the possible application in magnetooptic recording. Making use of symbolic computation, we figure out (1) a set of the variable-coefficient-dependent bilinear forms, (2) two sets of the variable-coefficient-dependent N-soliton solutions and (3) two sets of the variable-coefficient-dependent auto-Bäcklund transformations along with some solitons, with N denoting a positive integer. Our results, under the involved constraints, rely on the variable coefficients.