9 problems

The minimal surface equation admits contact symmetries $\varphi_k$ indexed by nonnegative integers $k$, with the relevant sequence introduced in the paper. Non-Noetherian contact s…

Let $m$ be the number of layers, let $c$ be the subalgebra parameter tuple, and let $\mathsf F$ and $\mathsf C$ be the matrices determining the model and the commutation relations.…

Singularity conjecture for $\mathcal F_n$. For each $n\in\mathbb N$, the equation $\mathcal F_n$ is singular within the class $\mathcal U_n$ and has the properties asserted in the…

Generalized symmetry algebra conjecture. Up to equivalence of generalized symmetries and after neglecting the Lie symmetries associated with the linear superposition of solutions,…

Let $\mathcal S$ be the isothermal no-slip drift flux system, let $\bar{\mathfrak A}=\langle\,(\mathscr J^\kappa q)\partial_q,\,\kappa\in\mathbb N\,\rangle$ be the complementary su…

For the two-dimensional incompressible inviscid Euler equations in vorticity formulation, the flow has infinitely many conservation laws. In an alternative Hamiltonian formulation,…

Let $\mathcal{L}_1$ be a maximal finite-dimensional superalgebra of Lie point symmetries of a nonlinear system of partial differential equations, and let $\mathcal{L}_2$ be a maxim…

Let the original nonlinear system have a set of symmetries, and let its associated linear system have another set of symmetries. In the finite-dimensional case, compare these sets…

Noether-to-Lie symmetry preservation conjecture. The passage from a classical system to its quantum analogue should preserve exactly those Noether symmetries: the Noether symmetrie…