Geometric Approaches to Differential Equations [Paperback]

A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.This book provides a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The aim of the book is to present an overview of this developing subject and a brief introduction to a number of related topics. Written by leading experts, this book is an ideal starting point for graduate students embarking on research. It will also be of use to researchers and anybody wishing to learn more about this burgeoning field of mathematical endeavour.This book provides a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The aim of the book is to present an overview of this developing subject and a brief introduction to a number of related topics. Written by leading experts, this book is an ideal starting point for graduate students embarking on research. It will also be of use to researchers and anybody wishing to learn more about this burgeoning field of mathematical endeavour.Here is a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The authors present an overview of this developing subject and introduce a number of related topics, including twistor theory, vortex filament dynamics, calculus of variations, exterior differential systems and Bäcklund transformations. The book is an ideal starting point for graduate students embarking on research.Preface; 1. Geometric approaches to differential equations: an introduction Peter J. Vassiliou; 2. B?cklund and his works: applications in soliton theory Colin Rogers, Wolfgang K. Schief and Mark E. Johnston; 3. Recent developments in integrable curve dynamics Annalisa Calini; 4. An elementary introduction to exterior differential systems Niky Kamran; 5. Cartan structure of infinite Lie pseudogroups Ian G. Lisle and Gregory J. Reid; 6. Carl#&