Differential invariants of nonlinear equations v_{tt} =f(x,v_x) v_{xx} + g(x,v_x)

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Nail H. Ibragimov, M. Torrisi, A. Valenti
Title: Differential invariants of nonlinear equations v_{tt} =f(x,v_x) v_{xx} + g(x,v_x)
Translated title: Differential invariants of nonlinear equations v_{tt} =f(x,v_x) v_{xx} + g(x,v_x)
Journal: Communications in Nonlinear Science and Numerical Simulation
Year: 2004
Volume: 9
Issue: 1
Pagination: 69-80
ISSN: 1007-5704
Publisher: Elsevier
City: The Netherlands
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
http://www.tek.bth.se/
Authors e-mail: nib@bth.se
Language: English
Abstract: We apply the infinitesimal technique for calculating invariants for the family of nonlinear equations formulated in the title. We show that the infinite-dimensional equivalence Lie algebra has three functionally independent differential invariants of the second order. Knowledge of invariants of families of equations is essential for identifying distinctly different equations and therefore for the problem of group classification.
Subject: Mathematics\Analysis
Keywords: Differential equations, Lie group analysis, differential invariants
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