7 problems

Let $S$ be an $N\times N$ matrix satisfying the cyclic constraint … Let $\mathcal{N}$ denote the recursion operator and let the local evolution equations be the local flows associa…

Let the systems under consideration be parametrized by $\beta=-1/\alpha$, where $\alpha$ is the parameter used in their original enumeration, and let a higher $\bar{s}$-symmetry me…

Maltsev–Novikov conjecture. The higher recursion operators $\mathfrak{R}^k$, higher Hamiltonian operators $\mathfrak{P}\circ\mathfrak{R}^\dagger{}^k$, and higher symplectic operato…

Let $\mathcal{R}^q$ and $\mathcal{R}^m$ be the basic recursion operators, and define, for $i,j\in\mathbb{Z}$, $\mathcal{R}_i^j$ by … with negative powers interpreted using the corr…

Let the rYME be the reduced quasi-classical self-dual Yang–Mills equation, and let the two constructed full-fledged recursion operators be denoted by $\mathcal{R}^q$ and…

Let ${\mathcal W} \subset {\mathcal V}$ be an integrable system. An integrable rational recursion operator is a rational operator $L=AB^{-1}$ satisfying the integrability condition…

Consider the potential Burgers equation … Let $D_x$ denote total differentiation with respect to $x$, and let $Q_1=u_x$, $Q_2=u_{xx}+\varepsilon u_x^2$, $Q_7=\varepsilon u_x$, and…