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Separation of Variables and Superintegrability

The symmetry of solvable systems
Willard Miller, Jr Jr, Ernest G Kalnins, Jonathan M Kress


Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting it in a unified, updated and a more accessible manner, the results scattered in the literature that the authors have prepared is an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.

About Editors

Earnest G Kalnins is a Professor at the University of Waikato in New Zealand. He is also a Fellow of the Royal Society of New Zealand and has published three books and more than 150 research papers. 

Jonathan M Kress is a  Senior Lecturer in the School of Mathematics and Statistics at the University of New South Wales in Australia. 

Willard J Miller is Emeritus Professor at University of Minnesota. He is also an AMS Fellow and author or co-author of three research monographs, two textbooks, two major review articles and more than 200 research papers.

Table of Contents

1 Introduction
2 Background and definitions
3 Separation of variables
4 Side condition separation
5 Separation for the real n-sphere
6 Separation for real Euclidean n-space
7 Separation on the hyperboloid
8 Conformally flat spaces
9 Time-dependent equations
10 Generalized Lie symmetries
11 Differential Stackel form
12 Functional separation
13 Vector equations
14 Links with r-matrix theory
15 Multiseparability


Hardback ISBN: 9780750313155

Ebook ISBN: 9780750313148

DOI: 10.1088/978-0-7503-1314-8

Publisher: Institute of Physics Publishing


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