Symmetry and explicit solutions of partial differential equations

DOI10.1016/0168-9274(92)90047-HzbMath0777.35017MaRDI QIDQ1195367

Peter J. Olver

Publication date: 25 October 1992

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetryLie group methoddifferential constraints

Mathematics Subject Classification ID

Lie groups (22E99) Solutions to PDEs in closed form (35C05)

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Uses Software

• SYMMGRP.MAX
• SPDE

Cites Work

• Automatically determining symmetries of partial differential equations
• Reduction and quotient equations for differential equations with symmetries
• Software to compute infinitesimal symmetries of exterior differential systems, with applications
• Reducing systems of linear differential equations to a passive form
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• On new exact blow-up solutions for nonlinear heat conduction equations with source and applications
• The computer calculation of Lie point symmetries of large systems of differential equations
• Computations in differential and difference modules
• The construction of special solutions to partial differential equations
• Non-classical symmetry reduction: example of the Boussinesq equation
• New similarity reductions of the Boussinesq equation
• Group-Invariant Solutions of Differential Equations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Finding abstract Lie symmetry algebras of differential equations without integrating determining equations
• The reducibility of partially invariant solutions of systems of partial differential equations
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
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