Two-magnon systems in the one-dimensional non-Heisenberg ferromagnet with nearest neighbours and second nearest neighbours interaction with spin value $s=1$

Two-magnon systems in the one-dimensional non-Heisenberg ferromagnet with nearest neighbours and second nearest neighbours interactions with a spin value $s=1$ are considered. It is shown that under $\Lambda=\pi $ and $\Lambda=0$ the system has no more than two, and under $\Lambda=\pi /2$ no more than six two-magnon bound states respectively.