Periodic Wave Solution and Its Stability in Antiferromagnet KCuF₃

Introducing the coherent state ansatz and the time-dependent variational principle, we obtain the two partial different equations of motion from Hamiltonian. Employing the method of multiple scales, we reduce these equations into the envelope function equation and find the amplitude function satisfied a nonlinear Schrödinger equation. We get the periodic wave solution and analyse its stability antiferromagnet KCuF₃.