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Advances in the Mathematical Sciences
The Interplay between Differential Geometry and Differential Equations
Edited by: V. V. Lychagin

American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
1995; 294 pp; hardcover
Volume: 167
ISBN-10: 0-8218-0428-6
ISBN-13: 978-0-8218-0428-5
List Price: US$125
Member Price: US$100
Order Code: TRANS2/167
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This work applies symplectic methods and discusses quantization problems to emphasize the advantage of an algebraic geometry approach to nonlinear differential equations. One common feature in most of the presentations in this book is the systematic use of the geometry of jet spaces.


Researchers and graduate students interested in nonlinear differential equations, differential geometry, quantum groups, and their applications.

Table of Contents

  • V. N. Chetverikov and A. G. Kudryavtsev -- Modeling integro-differential equations and a method for computing their symmetries and conservation laws
  • J. Donin and D. Gurevich -- Braiding of the Lie algebra \(sl(2)\)
  • B. Enriquez, S. Khoroshkin, A. Radul, A. Rosly, and V. Rubtsov -- Poisson-Lie aspects of classical \(W\)-algebras
  • N. G. Khor'kova and A. M. Verbovetsky -- On symmetry subalgebras and conservation laws for the \(k-\epsilon\) turbulence model and the Navier-Stokes equations
  • P. H. M. Kersten and I. S. Krasil'shchik -- Graded Frölicher-Nijenhuis brackets and the theory of recursion operators for super differential equations
  • A. Kushner -- Symplectic geometry of mixed type equations
  • V. Lychagin -- Homogeneous geometric structures and homogeneous differential equations
  • A. Prástaro -- Geometry of quantized super PDEs
  • A. V. Samokhin -- Symmetries of linear ordinary differential equations
  • N. A. Shananin -- Foliations of manifolds and weighting of derivatives
  • V. E. Shemarulin -- Higher symmetry algebra structures and local equivalences of Euler-Darboux equations
  • D. V. Tunitsky -- Hyperbolicity and multivalued solutions of Monge-Ampère equations
  • L. Zilbergleit -- Singularities of solutions of the Maxwell-Dirac equation
  • L. Zilbergleit -- Characteristic classes of Monge-Ampère equations
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