Differential invariants of the one-dimensional quasi-linear second-order evolution equation

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Nail H. Ibragimov, C. Sophocleus
Title: Differential invariants of the one-dimensional quasi-linear second-order evolution equation
Journal: Communications in Nonlinear Science and Numerical Simulation
Year: 2007
Volume: 12
Issue: 7
Pagination: 1133-1145
ISSN: 1007-5704
Publisher: Elsevier
City: Amsterdam
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/
Language: English
Abstract: We consider evolution equations of the form ut = f(x, u, ux)uxx + g(x, u, ux) and ut = uxx + g(x, u, ux). In the spirit of the recent work of Ibragimov [Ibragimov NH. Laplace type invariants for parabolic equations. Nonlinear Dynam 2002;28:125-33] who adopted the infinitesimal method for calculating invariants of families of differential equations using the equivalence groups, we apply the method to these equations. We show that the first class admits one differential invariant of order two, while the second class admits three functional independent differential invariants of order three. We use these invariants to determine equations that can be transformed into the linear diffusion equation.
Subject: Mathematics\Analysis
Keywords: Computer simulation, Diffusion, Invariance, Linear equations, Mathematical transformations
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