Summary: This note deals with the solutions defined for all time (i.e. entire) of \[ u_t= u_{xx}+ f(u),\quad 0< u(x,t)<1,\quad x\in\mathbb{R},\quad t\in\mathbb{R}, \] where \(f\) is a KPP type nonlinearity on \([0,1]\). This equation admits infinitely many travelling waves type solutions as well as solutions of the type \(u(t)\). We have build four other manifolds of solutions, the biggest one being five-dimensional. Furthermore, the travelling waves are on the boundary of these four manifolds. We also answer the question of the uniqueness for a certain class of solutions.