**Translations of Mathematical Monographs**

1999;
333 pp;
Hardcover

MSC: Primary 35;
Secondary 58

Print ISBN: 978-0-8218-0958-7

Product Code: MMONO/182

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-4596-6
Product Code: MMONO/182.E**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

# Symmetries and Conservation Laws for Differential Equations of Mathematical Physics

Share this page *Editors and Authors: *
*I. S. Krasil′shchik; A. M. Vinogradov; A. V. Bocharov; V. N. Chetverikov; S. V. Duzhin; N. G. Khor’kova; A. V. Samokhin; Yu. N. Torkhov; A. M. Verbovetsky*

This book presents developments in the geometric approach to
nonlinear partial differential equations (PDEs). The expositions
discuss the main features of the approach, and the theory of symmetries
and the conservation laws based on it. The book combines
rigorous mathematics with concrete examples. Nontraditional topics,
such as the theory of nonlocal symmetries and cohomological theory of
conservation laws, are also included.

The volume is largely self-contained and includes detailed
motivations, extensive examples and exercises, and careful proofs of
all results. Readers interested in learning the basics of applications
of symmetry methods to differential equations of mathematical physics
will find the text useful. Experts will also find it useful as it
gathers many results previously only available in journals.

#### Readership

Advanced graduate students and mathematicians working in nonlinear PDEs and their applications, mathematical and theoretical physics, and mechanics.

#### Reviews & Endorsements

A valuable feature about the present text is that it provides an overview of a number of results that originally appeared in Russian journals and are often difficult to track down. Moreover, the text is a useful reference for the practitioner in the field not only due to the descriptions of the various relevant algorithms but also due to the numerous examples involving symmetry algebras and conservation laws of particular equations, which, because of the book's emphasis on higher-order and potential symmetries, can often not be found in other standard references in the field. In all, this text provides a useful and readable introduction to the recent developments in the theory of symmetries and conservation laws of differential equations.

-- Mathematical Reviews

Rigorous mathematics and concrete examples illustrate the geometric approach to the study of nonlinear PDEs.

-- American Mathematical Monthly

#### Table of Contents

# Table of Contents

## Symmetries and Conservation Laws for Differential Equations of Mathematical Physics

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Ordinary differential equations 116
- First-order equations 3752
- The theory of classical symmetries 6984
- Higher symmetries 123138
- Conservation laws 185200
- Nonlocal symmetries 221236
- From symmetries of partial differential equations towards secondary ("quantized") calculus 301316
- Bibliography 323338
- Index 329344
- Back Cover Back Cover1353