Two-magnon states in a one-dimensional non-Heisenberg ferromagnet of spins = 1 with interactions up to third neighbors

We consider a two-magnon system in a one-dimensional non-Heisenberg ferromagnet of spin s = 1 with interactions of nearest, second, and third neighbors. We prove that for = and J = J₁, the system has a unique two-magnon bound state (TMBS), while for = and J = 2J₁, the system has three bound states. If = and J J₁, J 2J₁, the system has at most five TMBS. The energies of these bound states are evaluated.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 262–268, May, 1996.Translated by A. M. Semikhatov.