7 problems

Discrete Painlevé integrability conjecture. All the difference equations arising in this way are discrete Painlevé equations satisfying integrability criteria such as singularity c…

Consider an integrable hierarchy with a universal space Lax operator, and its type-I and type-II Bäcklund transformations. Universality conjecture. For a given hierarchy, both the…

Let $L$ be the Lax operator common to the entire hierarchy, and let $K$ be a gauge matrix defining a type-II Bäcklund transformation for one member of the hierarchy. Universality c…

Backlund reduction-diagram conjecture. Reducing $\mathcal{I}$ by $\Gamma_{G_1}$, $\Gamma_{G_2}$, and $\Gamma_H$ should produce a commutative diagram of Pfaffian systems with quotie…

Ragnisco–Zullo all-orders interpolation conjecture. For any fixed $bbda_0$, there exists a reparametrization $b5\to T_{\lambda_0}$, possibly depending on the integrals and Casimir…

Ragnisco–Zullo orbit-interpolation conjecture. Provided that $bbda0 ifully?$ and $b8 ifully?$, the two-point transformation has the same orbits as the continuous dynamical system g…

Ragnisco–Zullo interpolation conjecture. The maps are interpolated by a specific one-parameter family of Hamiltonian flows.