Lie-Backlund Transformations in Applications

✍ Scribed by Robert L. Anderson, Nail H. Ibragimov

• Publisher: Society for Industrial Mathematics
• Year: 1987
• Tongue: English
• Leaves: 135
• Series: Studies in Applied and Numerical Mathematics
• Category: Library

✦ Synopsis

This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of transformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.

✦ Table of Contents

Lie-Bäcklund Transformations in Applications......Page 2
Contents......Page 6
Preface......Page 8
Introduction......Page 10
1 Classical Foundations......Page 12
2 Tangent Transformation Groups......Page 48
3 Application to Differential Equations......Page 72
4 Some Applications of Bäcklund Transformations......Page 118
References......Page 130
Index......Page 134