AN INVERSE SCATTERING TRANSFORM FOR THE LANDAU-LIFSHITZ EQUATION FOR A SPIN CHAIN WITH AN EASY-PLANE

The Landau-Lifshitz equation for a spin chain with an easy plane in th e case of spin non-flip is solved by the method of inverse scattering transform. To avoid complexity caused by the Riemann surface of the us ual spectral parameter, a particular parameter k is introduced. After performing a gauge transformation corresponding to \k\ --> infinity, t he resulting Lax pair is independent of particular solutions in this l imit. An inverse scattering transform is then developed in terms of k. A system of linear equations is derived in the reflectionless case. A n expression of the gauge transformation and hence expressions of mult i-soliton solutions are found explicitly by using the Binet-Cauchy for mula As an example, an explicit expression of the I-soliton is given i n terms of elementary functions of x and t.