A nonhomogeneous boundary-value problem for the modified anisotropic heisenberg spin chain posed on a finite domain

This article is concerned with the Modified Anisotropic Heisenberg Spin Chain. We prove that the associated nonhomogeneous initial-boundary value problem has a unique globally smooth solution in H2k+1(m, n) for k >= 1. Our main new ingredient is a technique of spatial difference and crucial uni-formed estimates of the step-size h. Meanwhile, to prove the global existence, we overcome drawbacks which are not exist in corresponding Cauchy problem.