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Reduction of systems of nonlinear partial differential equations to simplified involutive forms

Published online by Cambridge University Press:  26 September 2008

Gregory J. Reid ,
Allan D. Wittkopf  and
Alan Boulton
Gregory J. Reid
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2
Allan D. Wittkopf
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2
Alan Boulton
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2
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Abstract

We describe an algorithm which uses a finite number of differentiations and algebraic operations to simplify a given analytic nonlinear system of partial differential equations to a form which includes all its integrability conditions. This form can be used to test whether a given differential expression vanishes as a consequence of such a system and may be more amenable to numerical or analytical solution techniques than the original system. It is also useful for determining consistent initial conditions for such a system. A computer implementable version of our algorithm is given for polynomially nonlinear systems of partial differential equations. This version uses Grobner basis techniques for constructing the radical of the polynomial ideal generated by the equations of such systems.

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Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 6 , December 1996 , pp. 635 - 666
Copyright
Copyright © Cambridge University Press 1996

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