A description of Lax type integrable dynamical systems via the Marsden–Weinstein reduction method

A Lie-algebraic approach to constructing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden–Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well known Adler–Kostant–Souriau–Berezin–Kirillov method and the associated R-matrix approach is analyzed.