3 problems

Let $P_i$, $A_i$, $r$, and $s$ be the parameters entering the ultra-discrete two-dimensional Toda lattice solution … where … An $(N_+,N_-)$-soliton is a resonant soliton solution o…

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