The book is both a textbook and a monograph. It is partially based on a two-semesters course on Analytical Mechanics, Differential Geometry, Symplectic Manifolds, Integrable Systems, and Electrodynamics, given by the author to third-year students in Physics and Mathematics.
As a textbook, it provides a systematic and self-consistent formulation of the Hamiltonian Dynamics in a first moment in a rigorous coordinates language, and after in the modern one of the Differential Geometry. It also supplies the reader with powerful mathematical methods of Theoretical Physics, especially Gauge...
The book is both a textbook and a monograph. It is partially based on a two-semesters course on Analytical Mechanics, Differential Geometry, Symplecti...
In the past decades now a famous class of evolution equations has been discovered and intensively studied, a class including the nowadays celebrated Korteweg-de Vries equation, sine-Gordon equation, nonlinear Schr] odinger equation, etc. The equations from this class are known also as the soliton equations or equations solvable by the so- called Inverse Scattering Tra- form Method. They possess a number of interesting properties, probably the most interesting from the geometric point of view of being that most of them are Liouville integrable Hamiltonian systems. Because of the importance of...
In the past decades now a famous class of evolution equations has been discovered and intensively studied, a class including the nowadays celebrated K...