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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.
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Hervé Leblond (2002) studied this question.
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