Stable three-dimensional small-amplitude solitons in magnetic materials

We investigate three-dimensional centrosymmetric soliton solutions of an equation of the nonlinear Schrödinger type, but which, unlike the standard situation, contains fourth (rather than second) derivatives with respect to the coordinates. An equation of this type affords a macroscopic description of quasiparticles whose effective mass becomes infinite. We show that, unlike the standard situation, three-dimensional small-amplitude solitons representing bound states of a large number of quasiparticles can exist in such a system. The energy associated with one quasiparticles in the bound state is smaller than the energy of a continuous-spectrum quasiparticle, evincing stability of the soliton.

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