Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties

Abstract

We consider the equations

\({u_{yy}} = {u_y}{u_{xx}} - ({u_x} + u){u_{xy}} + {u_x}{u_{y,}}{u_{yy}} = ({u_x} + {u_y}){u_{xy}} - ({u_{xx}} + 2){u_y}\)

that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of nonlocal symmetries in the infinite-dimensional coverings naturally associated to these equations.