Uniqueness conjecture for integrable viscous conservation laws

Let $a(u)$ be a non-vanishing functional parameter, and consider integrable viscous conservation laws obtained from the deformation procedure extended to arbitrary order in $\epsilon$, together with their normal forms and commuting flows associated with the 1-forms referred to in the source. Uniqueness conjecture for integrable viscous conservation laws. The normal form of these integrable viscous conservation laws and their commuting flows are uniquely determined at any order in $\epsilon$ by the non-vanishing functional parameter $a(u)$. The claim is supported by perturbative calculations; the supplied text does not state that it has been proved or disproved.