Abstract
Up to now, for a given PDE system, we have considered the calculation and application of its local symmetries (point, contact or higher-order) as well as the calculation of its local conservation laws. In particular, it has been shown how to use local symmetries to map solutions to other solutions; how to use local symmetries of given and target PDEs as an aid in relating them; how to use point or contact symmetries to determine whether a given PDE system can be mapped invertibly to some PDE system belonging to a target class of PDE systems that is completely characterized by its point symmetries as well as determine an explicit mapping when one exists; how to use multipliers yielding local conservation laws to determine whether a given nonlinear PDE system can be mapped invertibly to some linear PDE system as well as determine a specific mapping when one exists. Moreover, as it is well known, local symmetries can be used to find specific solutions (invariant solutions) of PDEs; this application is considered and extended in Chapter 5.
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© 2010 Springer-Verlag New York
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Bluman, G.W., Cheviakov, A.F., Anco, S.C. (2010). Nonlocally Related PDE Systems. In: Applications of Symmetry Methods to Partial Differential Equations. Applied Mathematical Sciences, vol 168. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68028-6_3
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DOI: https://doi.org/10.1007/978-0-387-68028-6_3
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98612-8
Online ISBN: 978-0-387-68028-6
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