Lie symmetries and conservation laws for a generalized Kuramoto‐Sivashinsky equation. (14th May 2018)

• Record Type: Journal Article
• Authors: Rosa, María; Camacho, Jose Carlos; Bruzón, María; Gandarias, María Luz
• Other Names: Aguiar Jesus Vigo guestEditor.; Rubio Raquel Garcia guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 17(2018)
• Page Start: 7295
• Page End: 7303
• Publication Date: 2018-05-14
• Subjects: conservation laws -- partial differential equations -- symmetry reductions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4825
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Nonlinear partial differential equations are used to describe complex phenomena in various fields of science. In this work, we consider a generalized fourth‐order nonlinear wave equation from the point of view of the theory of symmetry reductions in partial differential equations. We derive classical symmetries, and we obtain the reductions from the optimal system of subalgebras. We derive all the low‐order conservation laws, and we search for multipliers of the reduced ordinary differential equations that are invariant under a symmetry group to reduce directly the order of the equations.