Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds

This book provides a detailed exposition of modern Lie-algebraic theory of integrable nonlinear dynamic systems on manifolds and its applications to mathematical physics, classical mechanics and hydrodynamics. The authors have developed a canonical geometric approach based on differential geometric considerations and spectral theory, which offers solutions to many quantization procedure problems. Much of the material is devoted to treating integrable systems via the gradient-holonomic approach devised by the authors, which can be very effectively applied. This volume is aimed at graduate-level students, researchers and mathematical physicists whose work involves differential geometry, ordinary differential equations, manifolds and cell complexes, topological groups and Lie groups.