Integrable Systems

This book considers the theory of 'integrable' non-linear partial differential equations. The theory was developed at first by mathematical physicists but later mathematicians, particularly from the Soviet Union, were attracted to the field. In this volume are reprinted some fundamental contributions, originally published in Russian Mathematical Surveys, from some of the leading Soviet workers. Dr George Wilson has written an introduction intended to smooth the reader's path through some of the articles.

Introduction George Wilson
Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteweg-de Vries equations
Proof of a variational relation between the coefficients of the asymptotic expansion of the resolvent of a Sturm-Liouville equation
Non-linear equations of Korteweg-de Vries type, finite-zone linear operators and abelian varieties
Methods of algebraic geometry in the theory of non-linear equations
Algebraic curves and non-linear difference equations
The structure of Hamiltonian mechanics
What is the Hamiltonian formalism?
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