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Solitary Excitations in Antiferrornagnets AFeBr3

Introducing the Holstein–Primakoff transformation, the coherent-state ansatz and the time-dependent variation principle, we obtain two partial differential equations of motion. Employing the method of multiple scales, we reduce these equations into the envelope function equations and force the amplitude function to satisfy a nonlinear Schrödinger equation. Using the inverse-scattering transformation, we obtain the single-, two- and N-soliton solutions and discuss the gap soliton in antiferromagnets AFeBr3.