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Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

Published online by Cambridge University Press:  16 July 2009

G. W. Bluman  and
S. Kumei
G. W. Bluman
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, CanadaV6T 1Y4
S. Kumei
Affiliation:
Faculty of Textile Science and Technology, Shinshu University, Ueda, Nagano 386, Japan
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Abstract

An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are realized as appropriate local symmetries of a related auxiliary system. Examples include the Hopf-Cole transformation and the linearizations of a nonlinear heat conduction equation, a nonlinear telegraph equation, and the Thomas equations.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 3 , September 1990 , pp. 217 - 223
Copyright
Copyright © Cambridge University Press 1990

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References

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