... this powerful technique,trying as much as possible to make it a (computerizable) algorithm. Finally, weapply it to various PDEs in 1 + 1 dimensions, mostly taken from physics, some ofthem chaotic: ... follows:u0= f(C ), u1= f(C, Cx,Ct ), u2= f(C, Cx,Ct,Cxx,Cxt,Ctt,S ), Let us take an example.Example 4.1. The Kolmogorov-Petrovskii-Piskunov (KPP) equation [7 3, 99]E(u) ≡ but− ... relationsFj(u, x, t, U, X, T )=0,j= 1, 2 (7)with some transformation between (x, t) and (X, T ), in which Fjdepends onthe derivatives of u(x, t) and U(X, T ), such that the elimination of u (resp. U)between...