7 problems

Consider an integrable hierarchy of scalar conservation laws … which is a perturbation of the Riemann--Hopf hierarchy, and transform it to the Arsie--Lorenzoni--Moro normal form ……

Let a $\tau$-symmetric Hamiltonian perturbation of the Riemann--Hopf hierarchy be written in generalized standard form, with first Hamiltonian … Here $\mathcal{P}_k$ denotes the se…

Consider a deformation of the Riemann hierarchy … where the flow with respect to $t_1$ is in normal form: … with $c_\lambda(u)\in\mathbb C[[u]]$. Arsie–Lorenzoni–Moro conjecture. I…

Let a tau-symmetric deformation of the Riemann hierarchy be given. A normal Miura transformation is a Miura transformation of the type defined in the source that preserves the rele…

Let a tau-symmetric integrable Hamiltonian deformation of the Riemann hierarchy be considered modulo normal Miura-type transformations. Write $w_k=\partial_x^k w$. The canonical de…

Viscous central-invariant conjecture. Two integrable viscous conservation laws admitting the same viscous central invariant $a(u)$ are Miura equivalent.

Quasilinear-part conjecture. The quasilinear part of a viscous conservation law is uniquely determined by $a(u)$.