On the structure of conservation laws of (3+1)-dimensional wave equation

In this paper, a (3+1)-dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws. The symmetry operators are determined to find the reduced form of the considered equation. The non-local conservation theorems and multipl...

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Bibliographic Details
Published in:Arab journal of mathematical sciences 2018-07, Vol.24 (2), p.199-224
Main Authors: Hejazi, S. Reza, Lashkarian, Elham
Format: Article
Language:English
Subjects:
Boyer’s formulation
Conservation laws
Direct method
Lie symmetry
Noether’s theorem
Wave equation
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Summary:In this paper, a (3+1)-dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws. The symmetry operators are determined to find the reduced form of the considered equation. The non-local conservation theorems and multipliers approach are performed on the (3+1)-dimensional wave equation. We obtain conservation laws by using five methods, such as direct method, Noether’s method, extended Noether’s method, Ibragimov’s method; and finally we can derive infinitely many conservation laws from a known conservation law viewed as the last method. We also derive some exact solutions using some conservation laws Anco and Bluman (2002).
ISSN:1319-5166
DOI:10.1016/j.ajmsc.2018.04.002