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Using the Holstein-Primakoff transformation, the coherent state ansatz and the time-dependent variational principle, we obtain the two partial differential equations of motion from the Hamiltonian. Empolying the method of multiple scales, we reduce these equations into the envelope function equation and force the amplitude function to satisfy a nonlinear Schrodinger equation. Introducing the inverse-scattering transformation, we get the single soliton solution and investigate solitary magnon localization in antiferromagnet (AFM) KCuF3.