Pseudopotentials and symmetries of evolution equations (Q5896549)

Let us consider the equation \[ u_ t=F(x,t,u,u_ 1,...,u_ n),\quad u=u(x,t),\quad u_ i=\partial^ iu/dx^ i. \] Let \(\partial\) (resp. \(\partial_ t)\) be the total derivative with respect to x (resp. t). A Lie-Bäcklund transformation of (1) is a function \(\phi\) satisfying \[ \partial_ t\phi =D_{\phi}F,\quad D_{\phi}=\sum^{\infty}_{i=0}\partial^ i\phi \quad \partial /\partial u_ i. \] A non-local symmetry from the symmetry \(\phi\) is constructed.