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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.

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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