Symmetries and symmetry-invariant solutions of differential equations


One of the typical applications of symmetry methods in the study of differential equations is the searching for symmetry-invariant solutions. I present here a review of some of the principal techniques related to this idea, together with a comparison between the various approaches, paying special attention to the notion of conditional symmetry (with a careful distinction between some different definitions),and to the concept of λ-symmetry.The close relationship between λ-symmetries for PDE's and standard symmetries is also pointed out.

DOI Code: 10.1285/i15900932v23n2p15

Keywords: Diffrerential equations; Lie symmetries; Invariant solutions; $lambda$-symmetries

Classification: 58J70; 35A30

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