In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which,...

Multi-photon excitation states of poly-atomic molecules undergoing a self-interaction via Kerr effect related processes are of great interest today. Their successful study must be both analytical and by means of modern quantum field theoretical tools. This book deals with these and related topics by developing modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum-optical system.

These lecture notes are ideally suited to graduate mathematical physics and physics students, but can also be of interest to mathematicians involved in applied physics...

Multi-photon excitation states of poly-atomic molecules undergoing a self-interaction via Kerr effect related processes are of great interest today. Their successful study must be both analytical and by means of modern quantum field theoretical tools. This book deals with these and related topics by developing modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum-optical system.

These lecture notes are ideally suited to graduate mathematical physics and physics students, but can also be of interest to mathematicians involved in applied physics...

This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax...