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Type-II hidden symmetries for some nonlinear partial differential equations. (English) Zbl 1225.35015

Tenreiro Machado, J. A. (ed.) et al., Nonlinear science and complexity. Based on the 2nd conference on nonlinear science and complexity, NSC ’08, Porto, Portugal, July 28–31, 2008. Berlin: Springer (ISBN 978-90-481-9883-2/hbk; 978-90-481-9884-9/ebook). 61-66 (2011).
Summary: The type-II hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a Lie point symmetry. In this paper we analyze the connection between one of the methods analyzed in [B. Abraham-Shrauner and K. S. Govinder, J. Nonlinear Math. Phys. 13, No. 1–4, 612–622 (2006; Zbl 1110.35321)] and the weak symmetries of the partial differential equation in order to determine the source of these hidden symmetries. We consider some of the models presented in [loc. cit.] as well as a linear three-dimensional wave equation.
For the entire collection see [Zbl 1202.00103].

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35L05 Wave equation
58J70 Invariance and symmetry properties for PDEs on manifolds
22E70 Applications of Lie groups to the sciences; explicit representations

Citations:

Zbl 1110.35321

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