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

In 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...

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Bibliographic Details
Published inCommunications in nonlinear science & numerical simulation Vol. 140; p. 108438
Main Authors Bluman, George W., de la Rosa, Rafael
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2025
Subjects
Lie’s reduction of order algorithm
Nonlocal symmetries
Nonlocally related systems
Symmetry-based method
Symmetry-based method
Nonlocal symmetries
Nonlocally related systems
Lie’s reduction of order algorithm
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ISSN1007-5704
1878-7274
DOI10.1016/j.cnsns.2024.108438

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Summary:In 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. •Lie’s reduction method extended to partial differential equations.•Use of symmetry-based method.•Illustratives examples.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2024.108438