  Using Jacobi elliptic function addition formulas and summation identities we
obtain several static and moving periodic soliton solutions of a classical
anisotropic, discrete Heisenberg spin chain with and without an external
magnetic field. We predict the dispersion relations of these nonlinear
excitations and contrast them with that of magnons and relate these findings to
the materials realized by a discrete spin chain. As limiting cases, we discuss
different forms of domain wall structures and their properties.
