**Contemporary Mathematics**

Volume: 285;
2001;
205 pp;
Softcover

MSC: Primary 17; 20; 22; 34; 35; 39; 51; 53;

Print ISBN: 978-0-8218-2964-6

Product Code: CONM/285

List Price: $62.00

Individual Member Price: $49.60

**Electronic ISBN: 978-0-8218-7875-0
Product Code: CONM/285.E**

List Price: $62.00

Individual Member Price: $49.60

# The Geometrical Study of Differential Equations

Share this page *Edited by *
*Joshua A. Leslie; Thierry P. Robart*

This volume contains papers based on some of the talks given at the NSF-CBMS conference on “The Geometrical Study of Differential Equations” held at Howard University (Washington, DC). The collected papers present important recent developments in this area, including the treatment of nontransversal group actions in the theory of group invariant solutions of PDEs, a method for obtaining discrete symmetries of differential equations, the establishment of a group-invariant version of the variational complex based on a general moving frame construction, the introduction of a new variational complex for the calculus of difference equations and an original structural investigation of Lie-Bäcklund transformations. The book opens with a modern and illuminating overview of Lie's line-sphere correspondence and concludes with several interesting open problems arising from symmetry analysis of PDEs. It offers a rich source of inspiration for new or established researchers in the field.

This book can serve nicely as a companion volume to *Selected Topics in the
Geometrical Study of Differential Equations*, by Niky Kamran,
in the AMS series, CBMS Regional Conference Series in Mathematics.

#### Table of Contents

# Table of Contents

## The Geometrical Study of Differential Equations

- Contents vii8 free
- Foreword ix10 free
- Summary of the principal lectures xiii14 free
- An overview of Lie's line–sphere correspondence 118 free
- Application of Lie group analysis to a mathematical model which describes HIV transmission 1128
- Geometry and PDE on the Heisenberg group: a case study 2138
- Invariant evolutions of curves and surfaces and completely integrable Hamiltonian systems 2946
- On the fixed points of the Toda hierarchy 3956
- Group invariant solutions in mathematical physics and differential geometry 5168
- Discrete symmetries of differential equations 6178
- Integrable geometric evolution equations for curves 7188
- On integrability of evolution equations and representation theory 85102
- Symmetry groups, nonlinear partial differential equations, and generalized functions 101118
- Lie symmetries of differential-difference equations 111128
- On a variational complex for difference equations 121138
- The invariant variational bicomplex 131148
- On geometrically integrable equations and hierarchies of pseudo-spherical type 145162
- Inductive construction of moving frames 157174
- Orbit reduction of contact ideals and group-invariant variational problems 171188
- About the local and formal geometry of PDE 183200
- Open problems in symmetry analysis 195212

#### Readership

Graduate students and research mathematicians.