AN INVERSE SCATTERING TRANSFORM FOR THE LANDAU-LIFSCHITZ EQUATION FORA SPIN CHAIN WITH AN EASY-AXIS

An inverse scattering transform is developed to solve the Landau-Lifsc hitz equation for a spin chain with an easy axis. Instead of introduci ng the Riemann surface, which is required for double-valued functions of the usual spectral parameter lambda, the transform is developed by making use of an auxiliary parameter zeta. The Marchenko equation, sol iton solutions and asymptotic behaviours are derived. The results redu ce naturally to those for the isotropic chain when the anisotropy vani shes.