The natural extension to PDEs of Lie’s reduction of order algorithm for ODEs - Bluman, George W.; de la Rosa, Rafael (Communications in nonlinear science & numerical simulation, 2025)
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.