The natural extension to PDEs of Lie's reduction of order algorithm for ODEs

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URI: http://hdl.handle.net/10498/35481

DOI: 10.1016/J.CNSNS.2024.108438

ISSN: 1007-5704

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Author/s
Bluman, George W.; Rosa Silva, Rafael de laAuthority UCA
Date
2025
Department
Matemáticas
Source
Communications in Nonlinear Science and Numerical Simulation - 2025, Vol. 140
Abstract
n this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural extension of Lie's reduction of order algorithm for ordinary differential equations by looking at this algorithm from a different point of view. Many examples exhibit various situations that can arise.
Subjects
Lie's reduction of order algorithm; Nonlocal symmetries; Nonlocally related systems; Symmetry-based method
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 Internacional