Dark Sharma-Tasso-Olver Equations and Their Recursion Operators

A complete scalar classification for dark Sharma-Tasso-Olver's(STO's) equations is derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark STO systems, thus some special equations including symmetry equation and dual symmetry equation are obtained by selecting a free parameter. Furthermore, the recursion operators of STO equation and dark STO systems are constructed by a direct assumption method.