A System with a Recursion Operator but One Higher Local Symmetry of the Form $u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$

Abstract

We construct a recursion operator for the system $(u_t,v_t)=(u_4+v^2,1/5 v_4)$, for which only one local symmetry is known and we show that the action of the recursion operator on $(u_t,v_t)$ is a local function.