"Many-poled" r-matrix Lie algebras, Lax operators, and integrable systems

For each finite-dimensional simple Lie algebra g, starting from a general g. g-valued solution r (u, v) of the generalized non-dynamical classical Yang-Baxter equation, we construct "N-poled" infinite-dimensional Lie algebras (g) over tilde (-)(r),(N) of g-valued meromorphic functions with the poles in a fixed set of points nu(1), ... , nu(N). We apply the constructed algebras to the theory of finite-dimensional integrable systems and theory of soliton equations and obtain with their help the most general form of anisotropic chiral field-type equations as well as the most general form of integrable N-top systems and integrable cases of N interacting Kirchhoff systems. (C) 2014 AIP Publishing LLC.