KP lumps in ferromagnets: a three-dimensional KdV-Burgers model

The three-dimensional long-wave approximation for electromagnetic waves in saturated ferromagnetic media is considered, taking into account damping and inhomogeneous exchange. The wave evolution is governed by a (3 + 1)-dimensional generalization of the Korteweg-de Vries, Burgers, Kadomtsev-Petviashvili and Zabolotskaya-Khokhlov equations. Neglecting the damping, we give plane-soliton and line-lump solutions, and show that they are unstable.