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GEOMETRIC SYMMETRY TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

Part of: General theory of differentiable manifolds General higher-order equations and systems Partial differential equations on manifolds; differential operators Parabolic equations and systems Partial differential equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  11 December 2015

NAGHMANA TEHSEEN
NAGHMANA TEHSEEN*
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Victoria3086, Australia email [email protected]
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Abstract

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Keywords

Vessiot theoryFrobenius integrabilityPfaffian systemsolvable structuresgeometric partial differential equationsShannon entropyevolution equations

MSC classification

Primary: 35A30: Geometric theory, characteristics, transformations
Secondary: 58A17: Pfaffian systems 58A15: Exterior differential systems (Cartan theory) 58A10: Differential forms 58A20: Jets 58A30: Vector distributions (subbundles of the tangent bundles) 58J72: Correspondences and other transformation methods (e.g. Lie-Bäcklund) 35G20: Nonlinear higher-order equations 35K25: Higher-order parabolic equations 35K59: Quasilinear parabolic equations 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 342 - 344
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Prince, G. and Tehseen, N., ‘Evolution equations: Frobenius integrability, conservation laws and travelling waves’, J. Phys. A 48(40) (2015), 405205–405213.CrossRefGoogle Scholar
Tehseen, N., ‘Explicit solutions of PDE via Vessiot theory and solvable structures’, J. Phys. A 47(31) (2014), 315207–315225.CrossRefGoogle Scholar
Tehseen, N. and Broadbridge, P., ‘Fourth order diffusion equations with increasing entropy’, Entropy 14(7) (2012), 1127–1139.CrossRefGoogle Scholar
Tehseen, N. and Prince, G., ‘Integration of PDEs by differential geometric means’, J. Phys. A 46(10) (2013), 105201–105220.Google Scholar