Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations. (7th October 2015)

• Record Type: Journal Article
• Authors: Tsyfra, Ivan; Czyżycki, Tomasz
• Other Names: Naz R. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2015(2015)
• Publication Date: 2015-10-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2015/181275
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too.