%0 Journal Article 
%A Bluman, George W.
%A Rosa Silva, Rafael de la
%T The natural extension to PDEs of Lie's reduction of order algorithm for ODEs
%D 2025
%@ 1007-5704
%U http://hdl.handle.net/10498/35481
%X 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.
%K Lie's reduction of order algorithm
%K Nonlocal symmetries
%K Nonlocally related systems
%K Symmetry-based method
%~ Universidad de Cádiz