THE METHOD OF DARBOUX TRANSFORMATION MATRIX FOR SOLVING THE LANDAU-LIFSCHITZ EQUATION FOR A SPIN CHAIN WITH AN EASY-PLANE

The Landau-Lifschitz equation for a spin chain with an easy plane is s olved by the method of the Darboux transformation matrix. In terms of a particular parameter k, Jest solutions and Darboux matrices are gene rated in a recursive manner. The Jest solutions are shown to satisfy t he corresponding Lax equations by a suitable choice of the constants i nvolved in the Darboux matrices. A system of linear equations is deriv ed and can yield the expressions for multi-soliton solutions. Asymptot ic behaviour in the limits as t --> +/- infinity is derived. An expres sion of the one-soliton solution is given in terms of elementary funct ions of x and t, as an example.