Integrable systems : selected papers

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. Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteweg-de Vries equations / I.M. Gelfand and L.A. Dikii Proof of a variational relation between the coefficients of the asymptotic expansion of the resolvent of a Sturm-Liouville equation / B.V. Yusin Non-linear equations of Korteweg-de Vries type, finite-zone linear operators, and abelian varieties / B.A. Dubrovin, V.B. Matveer, and S.P. Novekov Methods of algebraic geometry in the theory of non-linear equations / I.M. Krichever Algebraic curves and non-linear difference equations / I.M. Krichever The structures of Hamiltonian mechanics / A.M. Vinogradov and B.A. Kupershmidt What is Hamiltonian formalism? / A.M. Vinogradov and I.S. Krasilshchik. "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"--Publisher's description