Reductions of the universal hierarchy and rdDym equations and their symmetry properties

Abstract

We consider the equations $u_{yy}=u_y{u}_{xx}-(u_x+u)u_{xy}+u_x{u}_y$ and $u_{yy}=(u_x+x)u_{xy}-(u_{xx}+2)u_y$ that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of nonlocal symmetries in infinite-dimensional coverings naturally associated to these equations.

References in corpus (6)

• Hydrodynamic reductions and solutions of a universal hierarchy
• Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type
• Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems
• Nonlocal symmetries of Lax integrable equations: a comparative study
• Integrability properties of some symmetry reductions
• 2D reductions of the equation $u_{yy}=u_{tx}+u_y{u}_{xx}-u_x{u}_{xy}$ and their nonlocal symmetries

Cited by in corpus (1)

• Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation