Integrable systems : selected papers

書誌事項

Integrable systems : selected papers

S.P. Novikov ... [et al.]

(London Mathematical Society lecture note series, 60)

Cambridge University Press, 1981

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注記

Includes bibliographical references

収録内容

  • 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

内容説明・目次

内容説明

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.

目次

  • Introduction George Wilson
  • 1. 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
  • 2. Proof of a variational relation between the coefficients of the asymptotic expansion of the resolvent of a Sturm-Liouville equation B. V. Yusin
  • 3. Non-linear equations of Korteweg-de Vries type, finite-zone linear operators and abelian varieties B. A. Dubrovin, V. B. Matveer and S. P. Novikov
  • 4. Methods of algebraic geometry in the theory of non-linear equations I. M. Krichever
  • 5. Algebraic curves and non-linear difference equations I. M. Krichever
  • 6. The structure of Hamiltonian mechanics A. M. Vinogradov and B. A. Kupershmidt
  • 7. What is the Hamiltonian formalism? A. M. Vinogradov and I. S. Krasilshchik.

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