Symmetries and reductions of order for certain nonlinear third- and second-order differential equations with arbitrary nonlinearity

摘要

We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to change from a nonlinearity with an arbitrary exponent to a nonlinearity with a specific numerical exponent. (C) 2015 AIP Publishing LLC.