Variational symmetries and conservation laws of the wave equation in one space dimension. (June 2020)

• Record Type: Journal Article
• Authors: Popovych, Roman O.; Cheviakov, Alexei F.
• Is Part Of: Applied mathematics letters. Volume 104(2020)
• Publication Date: 2020-06
• Subjects: Wave equation -- Variational symmetry -- Conservation law -- Noether's theorem -- Direct method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106225
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's theorem yields the space of variational symmetries of the corresponding functional. The results are also presented for the standard space–time form of the wave equation.