Explicit solutions in soliton theory using matrix boundary Riemann problem

Vector boundary Riemann problem with permutation matrix coefficient is proposed as analytic technique of the Landau-Lifshitz equation study. Spectral parameter of the latter varies on a hyperelliptic surface in the case of complete anisotropy and arbitrary finite genus of covering. Algebraic equations of coverings regarding the unknown vector field function are obtained as for the original problem statement, as for the most interesting non-Abelian (non-commutative) version caused by the initially given commutative condition.