Covering Surfaces with Noncommutative Monodromy Groups and their Industrial Applications

An explicit construction of the algebraic equations of the covering surfaces with the noncommutative monodromy groups is done by means of the corresponding homogeneous vector boundary Riemann-Hilbert problem solution. The direct applications concern soliton theory and Landau-Lifshitz equation, in particular. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)