On Classification of Symmetry Reductions for Partial Differential Equations †
1
Institute of Mathematics, Pedagogical University, 30-084 Cracow, Poland
2
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, 79053 Lviv, Ukraine
*
Author to whom correspondence should be addressed.
†
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 85; https://doi.org/10.3390/proceedings2010085
Published: 15 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)
Symmetry reduction is one of the most powerful tools for the investigation of partial differential equations. In particular, for this purpose, we can use a classical Lie method. To try to explain some of the differences in the properties of the reduced equations, we suggest investigating the relationship between the structural properties of nonconjugate subalgebras of the Lie algebras belonging to the symmetry groups of the equations under consideration and the properties of the reduced equations corresponding to them.In our talk, we plan to present some of the results concerning the relationship between the structural properties of low-dimensional (dim L ≤ 3) nonconjugate subalgebras of the Lie algebra of the generalized Poincaré group P(1,4) and the types of symmetry reduction for some P(1,4)-invariant equations in the space M(1,3) × R(u). More details on this theme can be found in:Fedorchuk V., Fedorchuk V. On Classification of Symmetry Reductions for the Eikonal Equation. Symmetry, 2016, 8, Art. 51, 32pp; doi:10.3390/sym8060051.
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Fedorchuk, V.; Fedorchuk, V. On Classification of Symmetry Reductions for Partial Differential Equations. Proceedings 2018, 2, 85. https://doi.org/10.3390/proceedings2010085
AMA Style
Fedorchuk V, Fedorchuk V. On Classification of Symmetry Reductions for Partial Differential Equations. Proceedings. 2018; 2(1):85. https://doi.org/10.3390/proceedings2010085
Chicago/Turabian StyleFedorchuk, Vasyl, and Volodymyr Fedorchuk. 2018. "On Classification of Symmetry Reductions for Partial Differential Equations" Proceedings 2, no. 1: 85. https://doi.org/10.3390/proceedings2010085
