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

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

2004-03-17

arxiv.org/abs/nlin/0403034v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, no figures

Scientific paper

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 existence of such conserved densities is a necesary condition for integrability in the sense of admitting a formal symmetry, hence integrable scalar evolution equations of order $m\ge 7$ are quasilinear.

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