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Polynomial and non-polynomial solutions set for wave equation using Lie point symmetries. (English) Zbl 1424.35127
Summary: This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE). We calculate polynomial and non-polynomial exact solutions by using Lie point symmetry. We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation. A generalized procedure for polynomial solution is presented and extended to the construction of related polynomials.

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
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