Messanae Universitas Studiorum

When Nonautonomous Equations are Equivalent to Autonomous Ones

Donato, Andrea and Oliveri, Francesco (2000) When Nonautonomous Equations are Equivalent to Autonomous Ones. Memorie scientifiche di Andrea Donato, LXXVII. pp. 541-551.

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Abstract

We consider nonlinear systems of first order partial differential equations admitting at least two one-parameter Lie groups of transformations with commuting infinitesimal operators. Under suitable conditions it is possible to introduce a variable transformation based on canonical variables which reduces the model in point to autonomous form. Remarkably, the transformed system may admit costant solutions to which three correspond non-costant solutions of the original model. The results are specialized to the case of first order quasilinear systems admitting either dilatation or spiral groups of transformations and a systematic procedure to characterize special exact solutions is given. At the end of the paper the equations of axi-symmetric gas dynamics are considered.

Item Type: Article
Subjects: M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 2000-01 > Supplemento 1
Depositing User: Utente Interno
Date Deposited: 01 Jun 2004
Last Modified: 14 Sep 2012 11:22
URI: http://cab.unime.it/mus/id/eprint/82

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