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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 066, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.066 (Mi sigma624) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction

Stephen C. Ancoa, Sajid Alib, Thomas Wolfa

a Department of Mathematics, Brock University, St. Catharines, ON L2S 3A1 Canada
b School of Electrical Engineering and Computer Sciences, National University of Sciences and Technology, H-12 Campus, Islamabad 44000, Pakistan
Full-text PDF (323 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2011.066
Abstract: A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation.
Keywords: semilinear heat equation; similarity reduction; exact solutions; group foliation; symmetry.
Received: March 5, 2011; in final form July 3, 2011; Published online July 12, 2011
Bibliographic databases:
Document Type: Article
MSC: 35K58; 35C06; 35A25; 58J70; 34C14
Language: English
Citation: Stephen C. Anco, Sajid Ali, Thomas Wolf, “Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction”, SIGMA, 7 (2011), 066, 10 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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