Exact solutions of (3+1)-dimensional wave equation via Lie brackets of symmetries

Document Type : Original Paper

Authors

Department of Mathematical Sciences, Shahrood university of Technology

Abstract

‎In this paper, the Lie symmetry method and Lie brackets of vector fields are used in order to find some new solutions of the (3+1)-dimensional sourceless wave equation‎. ‎The obtained solutions are classified into two categories; polynomial and non-polynomial exact solutions‎. ‎Because of the properties of the Lie brackets and the symmetries‎, ‎a generalized method is implemented for constructing new solutions from old solutions‎. ‎We demonstrate the generation of such polynomial and non-polynomial solutions through the medium of the group theoretical properties of the equation‎. ‎It is noteworthy that this method could be used when the equations have two special kinds of symmetries which will be mentioned below‎.

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