**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

1995; 294 pp; Hardcover

MSC: Primary 17; 35; 58;

Print ISBN: 978-0-8218-0428-5

Product Code: TRANS2/167

Print ISBN: 978-0-8218-0428-5

Product Code: TRANS2/167

List Price: $125.00

Individual Member Price: $100.00

**Electronic ISBN: 978-1-4704-3378-9
Product Code: TRANS2/167.E**

List Price: $125.00

Individual Member Price: $100.00

# The Interplay between Differential Geometry and Differential Equations

Share this page *Edited by *
*V. V. Lychagin*

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.

#### Readership

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

# Table of Contents

## The Interplay between Differential Geometry and Differential Equations

- Cover Cover11
- Title page v6
- Copyright page vi7
- Contents vii8
- Foreword ix10
- Modeling integro-differential equations and a method for computing their symmetries and conservation laws 112
- Braiding of the Lie algebra 𝑠𝑙(2) 2334
- Poisson-Lie aspects of classical 𝑊-algebras 3748
- On symmetry subalgebras and conservation laws for the 𝑘-𝜀 turbulence model and the Navier–Stokes equations 6172
- Graded Frölicher–Nijenhuis brackets and the theory of recursion operators for super differential equations 91102
- Symplectic geometry of mixed type equations 131142
- Homogeneous geometric structures and homogeneous differential equations 143154
- Geometry of quantized super PDE’s 165176
- Symmetries of linear ordinary differential equations 193204
- Foliations of manifolds and weighting of derivatives 207218
- Higher symmetry algebra structures and local equivalences of Euler–Darboux equations 217228
- Hyperbolicity and multivalued solutions of Monge–Ampère equations 245256
- Singularities of solutions of the Maxwell–Dirac equation 261272
- Characteristic classes of Monge–Ampère equations 279290
- Back Cover Back Cover1306