A METHOD FOR SOLVING THE EQUATION OF A FERROMAGNETIC CHAIN AND VERIFICATION OF THE TAKHTAJAN EQUATION

Based on the gauge equivalence, we solve the equation of a Heisenberg ferromagnetic chain by using the inverse scattering method of the nonlinear Schrodinger equation and an explicitly obtained form of the required gauge transformation. We show that the solutions of a ferromagnetic chain by the Takhtajan's method identify with that by the above mentioned method. Then we prove the correctness of the Takhtajan equation and avoid the defects in its derivations.