تعامل بین هندسه دیفرانسیل و معادلات دیفرانسیل (سری ترجمه‌های انجمن ریاضی آمریکا ۲)

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. Modeling Integro-differential Equations And A Method For Computing Their Symmetries And Conservation Laws / V.n. Chetverikov And A.g. Kudryavtsev -- Braiding Of The Lie Algebra Sl(2) / J. Donin And D. Gurevich -- Poisson-lie Aspects Of Classical W-algebras / B. Enriquez, S. Khoroshkin, A. Radul, A. Rosly And V. Rubtsov -- On Symmetry Subalgebras And Conservation Laws For The K - [e] Turbulence Model And The Navier-stokes Equations / N.g. Khorʹkova And A.m. Verbovetsky -- Graded Frölicher-nijenhuis Brackets And The Theory Of Recursion Operators For Super Differential Equations / P.h.m. Kersten And I.s. Krasilʹshchik -- Symplectic Geometry Of Mixed Type Equations / A. Kushner -- Homogeneous Geometric Structures And Homogeneous Differential Equations / V. Lychagin -- Geometry Of Quantized Super Pde's / Agostino Prástaro -- Symmetries Of Linear Ordinary Differential Equations / Alexey V. Samokhin -- Foliations Of Manifolds And Weighting Of Derivatives / N.a. Shananin -- Higher Symmetry Algebra Structures And Local Equivalences Of Euler-darboux Equations / Valery E. Shemarulin -- Hyperbolicity And Multivalued Solutions Of Monge-ampère Eequations / D.v. Tunitsky -- Singularities Of Solutions Of The Maxwell-dirac Equation / L. Zilbergleit -- Characteristic Classes Of Monge-ampère Equations / L. Zilbergleit . V.v. Lychagin, Editor. Includes Bibliographical References. Contents Foreword • V. LYCHAGIN Modeling Integro-Differential Equations and a Method for Computing their Symmetries and Conservation Laws • V. N. CHETVERIKOV and A. G. KUDRYAVTSEV Braiding of the Lie Algebra si (2) • J. DONIN and D. GUREVICH Poisson-Lie Aspects of Classical W-Algebras • B. ENRIQUEZ, S. KHOROSHKIN, A. RADUL, A. ROSLY, and V. RUBTSOV On Symmetry Subalgebras and Conservation Laws for the κ — ε Turbulence Model and the Navier-Stokes Equations • N. G. KHOR'KOVA and A. M. VERBOVETSKY Graded Frölicher-Nijenhuis Brackets and the Theory of Recursion Operators for Super Differential Equations • R H. M. KERSTEN and I. S. KRASIL’SHCHIK Symplectic Geometry of Mixed Type Equations • A. KUSHNER Homogeneous Geometric Structures and Homogeneous Differential Equations • V. LYCHAGIN Geometry of Quantized Super PDE’s • AGOSTINO PRASTARO Symmetries of Linear Ordinary Differential Equations • ALEXEY V. SAMOKHIN Foliations of Manifolds and Weighting of Derivatives • N. A. SHANANIN Higher Symmetry Algebra Structures and Local Equivalences of Euler-Darboux Equations • VALERY E. SHEMARULIN Hyperbolicity and Multivalued Solutions of Monge-Ampère Equations • D. V. TUNITSKY Singularities of Solutions of the Maxwell-Dirac Equation • L. ZILBERGLEIT Characteristic Classes of Monge-Ampère Equations • L. ZILBERGLEIT Discusses quantization problems to emphasize the advantage of an algebraic geometry approach to nonlinear differential equations. This book features systematic use of geometry of jet spaces.