Symmetries and reductions of order for certain nonlinear third and second-order differential equations with arbitrary nonlinearity
arXiv:1504.00105
Abstract
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.