  NiCl$_2$-4SC(NH$_2$)$_2$ (DTN) is a quantum S=1 chain system with strong
easy-pane anisotropy and a new candidate for the Bose-Einstein condensation of
the spin degrees of freedom. ESR studies of magnetic excitations in DTN in
fields up to 25 T are presented. Based on analysis of the single-magnon
excitation mode in the high-field spin-polarized phase and previous
experimental results [Phys. Rev. Lett. 96, 077204 (2006)], a revised set of
spin-Hamiltonian parameters is obtained. Our results yield $D=8.9$ K, $J_c=2.2$
K, and $J_{a,b}=0.18$ K for the anisotropy, intrachain, and interchain exchange
interactions, respectively. These values are used to calculate the
antiferromagnetic phase boundary, magnetization and the frequency-field
dependence of two-magnon bound-state excitations predicted by theory and
observed in DTN for the first time. Excellent quantitative agreement with
experimental data is obtained.
