Abstract
It is shown how Lie group and Lie algebra theory can be used to solve partial differential equations. A method for calculating the symmetry group of a set of differential equations is presented. Special attention is devoted to algorithms for classifying subalgebras of Lie algebras. The concept of conditional symmetries is introduced and applied to perform dimensional reduction.
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Winternitz, P. Lie groups, singularities and solutions of nonlinear partial differential equations. In: Direct and Inverse Methods in Nonlinear Evolution Equations. Lecture Notes in Physics, vol 632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39808-0_5
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DOI: https://doi.org/10.1007/978-3-540-39808-0_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20087-1
Online ISBN: 978-3-540-39808-0
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