George W. Bluman, Alexei F. Cheviakov, Stephen C. Anco (auth.)9780387986128, 038798612X
This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete “adjoint symmetries,” Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful.
This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications.
Table of contents :
Front Matter….Pages 1-18
Local Transformations and Conservation Laws….Pages 1-120
Construction of Mappings Relating Differential Equations….Pages 121-186
Nonlocally Related PDE Systems….Pages 187-244
Applications of Nonlocally Related PDE Systems….Pages 245-296
Further Applications of Symmetry Methods: Miscellaneous Extensions….Pages 297-367
Back Matter….Pages 1-29
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