The present survey is devoted to a general group-theoretic scheme which allows to
construct integrable Hamiltonian systems and their solutions in a systematic way. This …

Symmetry has always played an important role in mechanics, from fundamental formulations
of basic principles to concrete applications. The theme of the book is to develop the basic …

Reduction theory for mechanical systems with symmetry has its roots in the classical works
in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré, and others. The …

The use of geometric methods in classical mechanics has proven fruitful, with wide
applications in physics and engineering. In this book, Professor Marsden concentrates on …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

The review is based on the authro's papers since 1985 in which a new approach to the
separation of variables (SoV) has being developed. It is argued that SoV, understood …

This invaluable book examines qualitative and quantitative methods for nonlinear differential
equations, as well as integrability and nonintegrability theory. Starting from the idea of a …

Many of the familiar integrable systems of equations are symmetry reductions of self-duality
equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries …

In this volume readers will find for the first time a detailed account of the theory of symplectic
reduction by stages, along with numerous illustrations of the theory. Special emphasis is …

This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists,
graduate students and professionals. The main thrust of the book is to show how algebraic …