On the Classification of Scalar Non-Polynomial Evolution Equations: Quasilinearity

Ayse Humeyra Bilge

We prove that, for $m\ge 7$, scalar evolution equations of the form $u_t=F(x,t,u,...,u_m)$ which admit a nontrivial conserved density of order $m+1$ are linear in $u_m$. The existe…