GEOMETRIC SYMMETRY TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

DOI10.1017/S0004972715001409zbMath1339.35015OpenAlexW2234222703WikidataQ115336877 ScholiaQ115336877MaRDI QIDQ2800105

Naghmana Tehseen

Publication date: 14 April 2016

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972715001409

zbMATH Keywords

evolution equationsShannon entropyPfaffian systemgeometric partial differential equationsVessiot theoryFrobenius integrabilitysolvable structures

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Pfaffian systems (58A17) Nonlinear higher-order PDEs (35G20) Jets in global analysis (58A20) Differential forms in global analysis (58A10) Exterior differential systems (Cartan theory) (58A15) Geometric theory, characteristics, transformations in context of PDEs (35A30) Vector distributions (subbundles of the tangent bundles) (58A30) Higher-order parabolic equations (35K25) Quasilinear parabolic equations (35K59) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Cites Work

• Fourth order diffusion equations with increasing entropy
• Explicit solutions of PDE via Vessiot theory and solvable structures
• Evolution equations: Frobenius integrability, conservation laws and travelling waves
• Integration of PDEs by differential geometric means

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