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 inArab journal of mathematical sciences Vol. 24; no. 2; pp. 199 - 224
Main Authors Hejazi, S. Reza, Lashkarian, Elham
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2018
Emerald Publishing
Subjects
Boyer’s formulation
Conservation laws
Direct method
Lie symmetry
Noether’s theorem
Wave equation
Wave equation
Conservation laws
Direct method
Noether’s theorem
70H33
Boyer’s formulation
76M60
35J05
Lie symmetry
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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