Bluman G.W., Cheviakov A.F., Anco S.C. Applications of Symmetry Methods to Partial Differential Equations

New York: Springer, 2010. — 398 p. — ISBN: 978-0-387-98612-8 e-ISBN: 978-0-387-68028-6.Local Transformations and Conservation LawsLocal Transformations
Conservation Laws
Noether's Theorem
Some Connections Between Symmetries and Conservation LawsConstruction of Mappings Relating Differential EquationsNotations; Mappings of Infinitesimal Generators
Mapping of a Given PDE to a Specific Target PDE
Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Symmetries
Invertible Mappings of Linear PDEs to Linear PDEs with Constant Coe±cients
Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Conservation Law MultipliersNonlocally Related PDE SystemsNonlocally Related Potential Systems and Subsystems in Two Dimensions
Trees of Nonlocally Related PDE Systems
Nonlocal Conservation Laws
Extended Tree Construction ProcedureApplications of Nonlocally Related PDE SystemsNonlocal Symmetries
Construction of Non-invertible Mappings Relating PDEsFurther Applications of Symmetry Methods: Miscellaneous ExtensionsApplications of Symmetry Methods to the Construction of Solutions of PDEs
Nonlocally Related PDE Systems in Three or More Dimensions
Symbolic Software