NONLINEAR EXCITATIONS IN THE CLASSICAL CONTINUUM ANTIFERROMAGNETIC HEISENBERG SPIN CHAIN

The nonlinear excitations in a one-dimensional classical isotropic continuum Heisenberg antiferromagnetic spin chain are studied by treating the chain as a two-sublattice problem. The dynamics is analyzed in detail at the lowest order, O(a) (with lattice constant a), of the continuum limit which involves only first derivatives. A general class of solutions is obtained for the equation of motion at this order. It is found that recently reported twist and instanton solutions are a special class of this general solution. The analysis is extended to the next higher order, O(a2), to investigate the effect of discreteness on the solutions obtained in the lowest order.