Algorithmic calculus for Lie determining systems

DOI10.1016/j.jsc.2016.03.002zbMath1361.35012OpenAlexW2330713426MaRDI QIDQ507157

S.-L. Tracy Huang, Ian G. Lisle

Publication date: 3 February 2017

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2016.03.002

zbMATH Keywords

algorithmLie algebradifferential eliminationLie symmetrydetermining equationsstructure constants

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Structure theory for Lie algebras and superalgebras (17B05) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (3)

On the algorithmic linearizability of nonlinear ordinary differential equations ⋮ Symmetry-based algorithms for invertible mappings of polynomially nonlinear PDE to linear PDE ⋮ LieAlgebrasOfVectorFields

Uses Software

• GeM
• Maple
• SADE
• DifferentialGeometry
• Janet

Cites Work

• [SADE a Maple package for the symmetry analysis of differential equations]
• GeM software package for computation of symmetries and conservation laws of differential equations
• On the structure of Lie pseudo-groups
• Applications of symmetry methods to partial differential equations
• An algorithm for determining the size of symmetry groups
• Geometry and structure of Lie pseudogroups from infinitesimal defining systems
• The infinite groups of Lie and Cartan. I: The transitive groups
• An orderly linear PDE system with analytic initial conditions with a non-analytic solution.
• Symmetry and integration methods for differential equations
• Symbolic computation and differential equations: Lie symmetries
• Structure of symmetry of PDE
• New symbolic tools for differential geometry, gravitation, and field theory
• Reduction of systems of nonlinear partial differential equations to simplified involutive forms
• Using Algebraic Geometry
• Homomorphisms of Continuous Pseudogroups
• Quotients of Pseudo Groups by Invariant Fiberings
• Recognizing the symmetry type of O. D. E. s
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