3 problems

Let $J,K\in\mathbb{R}$ and let $F_{udK}^{(J,K)}:\mathbb{R}^2\to\mathbb{R}^2$ be the ultra-discrete KdV map in the source. For $c<\min\{J/2,K/2\}$ and $c_1,c_2<\min\{J/2,K/2\}$, con…

Ultra-discrete KdV detailed-balance conjecture. The variables $U$ and $V$ should be independent if and only if there exist $\lambda,c_1,c_2>0$ such that

DLYZ's quasi-Miura conjecture. At $s=1$, this quasi-Miura map gives rise to an explicit deformation of the discrete KdV hierarchy.