Iterating the classical symmetries method to solve initial value problems

This paper demonstrates how the infinite‐dimensional part of the classical symmetry algebra of linear partial differential equations can be used to find solutions to initial value problems. We can formulate a secondary initial value problem whose solution, when augmented to a pre‐specified infinitesimal Lie point symmetry, as a one‐parameter superposition, produces a symmetry that is compatible with the original initial condition. This secondary initial value problem may be easier to solve than the original. If not, we can iterate the process to generate a third or subsequent initial value problem.