New integrable Gaudin-type systems, classical r-matrices and quasigraded Lie algebras

Abstract

For each non-skew classical r-matrix with the spectral parameter we construct an integrable classical Gaudin-type system. Using special quasigraded Lie algebras we explicitly construct new non-skew classical r-matrices with the spectral parameter and obtain with their help explicit form of new integrable classical Gaudin-type systems.