The use of factors to discover potential systems or linearizations
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Publication:1903553
DOI10.1007/BF00996104zbMath0841.35005OpenAlexW4245482011MaRDI QIDQ1903553
George W. Bluman, Patrick Doran-Wu
Publication date: 11 December 1995
Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00996104
Nonlinear parabolic equations (35K55) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Group structures and generalizations on infinite-dimensional manifolds (58B25)
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Cites Work
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- Symmetries and conservation laws of partial differential equations: Basic notions and results
- Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations
- Automatically determining symmetries of partial differential equations
- Nonlocal symmetries and the theory of coverings: An addendum to A. M. Vinogradov's 'Local Symmetries and Conservation Laws'
- Similarity methods for differential equations
- Use and construction of potential symmetries
- The computer calculation of Lie point symmetries of large systems of differential equations
- On invariance properties of the wave equation
- New classes of symmetries for partial differential equations
- Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
- When Nonlinear Differential Equations are Equivalent to Linear Differential Equations
- Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
- Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries
- Symmetries and differential equations
