Solutions to nonlinear partial differential equations from symmetry-enhancing and symmetry-preserving constraints

DOI10.1006/jmaa.1999.6505zbMath0935.35023OpenAlexW2077836964MaRDI QIDQ1125297

Philip Broadbridge, Joanna M. Goard

Publication date: 9 February 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6505

zbMATH Keywords

Navier-Stokes equationsexplicit solutionLie point symmetriesboundary layer equationdifferential constraints

Mathematics Subject Classification ID

Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05)

Uses Software

• SYMMGRP
• diffgrob2

Cites Work

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• Review of symbolic software for Lie symmetry analysis
• Nonlinear superposition principles obtained by Lie symmetry methods
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• Nonlinear partial differential equations in engineering. Vol. II
• New similarity reductions of the Boussinesq equation
• Similarity reductions of partial differential equations
• New similarity reductions of the steady-state boundary layer equations
• Nonclassical symmetry solutions and the methods of Bluman–Cole and Clarkson–Kruskal
• THE CONSTRUCTION OF SPECIAL EXPLICIT SOLUTIONS OF THE BOUNDARY-LAYER EQUATIONS. STEADY FLOWS
• Direct reduction and differential constraints
• New exact solutions of Burgers’s equation—an extension to the direct method of Clarkson and Kruskal
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I

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