Separation of variables and superintegrability :the symmetry of solvable systems /

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Separation of variables and superintegrability :the symmetry of solvable systems /

Kalnins, E. G., - Personal Name; Institute of Physics (Great Britain), - Personal Name; Kress, Jonathan M., - Personal Name; Miller, Willard, - Personal Name;

"Version: 20180501"--Title page verso.Includes bibliographical references.1. Introduction -- 2. Background and definitions -- 2.1. Classical mechanics -- 2.2. Quantum mechanics -- 2.3. Integrability and superintegrability3. Separation of variables -- 3.1. Some approaches to separability -- 3.2. The Levi-Civita procedure -- 3.3. Nonorthogonal separation : examples -- 3.4. Intrinsic characterization of separation4. Side condition separation -- 4.1. A generalization of St?ackel form -- 4.2. Generalized Helmholtz St?ackel form -- 4.3. Maximal non-regular separation -- 4.4. Examples of non-regular separability5. Separation for the real n-sphere -- 5.1. Jacobi elliptic coordinates -- 5.2. Killing vectors and tensors6. Separation for real Euclidean n-space -- 6.1. Elliptic coordinates in Euclidean space -- 6.2. Parabolic coordinates in Euclidean space -- 6.3. Construction of all separable coordinates -- 6.4. Comments and references7. Separation on the hyperboloid -- 7.1. Branching rules for hyperbolic n-space -- 7.2. Separation for hyperbolic three-space8. Conformally flat spaces -- 8.1. Hyperspherical coordinates -- 8.2. Separable coordinates : analytic theory -- 8.3. Separable coordinates : algebraic theory -- 8.4. Comments and references9. Time-dependent equations -- 9.1. Case (i) : time as ignorable variable -- 9.2. Case (ii) : time-dependent Hamiltonians -- 9.3. Coordinates on spheres and Euclidean spaces -- 9.4. Examples10. Generalized Lie symmetries -- 11. Differential St?ackel form -- 11.1. Separation of Laplace equations12. Functional separation -- 12.1. A forced wave equation -- 12.2. Pseudo-Riemannian spaces13. Vector equations -- 13.1. Dirac-type equations14. Links with r-matrix theory -- 14.1. Complex constant curvature spaces -- 14.2. Generic ellipsoidal coordinates -- 14.3. Cyclidic coordinates15. Multiseparability -- 15.1. 2D superintegrable systems -- 15.2. Canonical equations -- 15.3. 3D superintegrable systems -- 15.4. Conclusions and extensions.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.Graduate students and researchers in mathematical physics.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Earnest G. Kalnins is a Professor at The University of Waikato, Hamilton, 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 Sydney, Australia. Willard J. Miller is an 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.Title from PDF title page (viewed on July 11, 2018).

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Series Title: -
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Publisher: : .,
Collation: 1 online resource (various pagings) :illustrations (some color).
Language: English
ISBN/ISSN: 9780750313148
Classification: 515.3/53
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Edition: -
Subject(s): SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Separation of variables.
Differential equations, Partial
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Statement of Responsibility: Ernest G. Kalnins, Jonathan M. Kress, Willard Miller Jr.

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