11 problems

Let $H^n$ be the Heisenberg group with $n>1$, and let … The critical exponent is … where $Q$ is the homogeneous dimension. A divergence symmetry is a Lie point symmetry whose actio…

For positive integers $m$ and $n$, consider the nonlinear Schrödinger systems whose arbitrary element has the form … where $\sigma$ is a nonzero constant, $\gamma=4/n$, and $v$,…

Let $\mathcal{G}$ be the Lie group of nonlocal symmetry diffeomorphisms associated with the integrable map … . Let its Lie algebra of generators be the Lie algebra of the correspon…

The integrable map corresponding to the linear equation, respectively the nonlinear equation, is denoted by … . A nonlocal diffeomorphism is a diffeomorphism whose action is nonloc…

Hierarchy conjecture. A hierarchy of Lie remarkable third-order systems involving the unknowns $u_\alpha(x_1,x_2)$ may exist.

A soliton hierarchy consists of commuting soliton equations, and suppose each equation has infinitely many functionally independent Lie symmetries inherited from a recursion operat…

Let a maximally symmetric space have non-vanishing curvature, and consider the Lie symmetries of its system of affinely parameterized geodesic equations. Feroze et al.'s conjecture…

Let $\mathcal{G}$ be the Lie group of nonlocal symmetry diffeomorphisms associated with the integrable map (respectively, ), and let and denote the corresponding continuous dynamic…

Let the integrable maps defined by equations and be given, and let $\mathcal{G}$ denote a Lie group of nonlocal diffeomorphisms. Nonlocal symmetry conjecture. The integrable map (r…

Maximal-symmetry conjecture. Maximally symmetric spaces of non-vanishing curvature do not admit further Lie symmetries.

A system of two second-order r-CODEs is considered, together with its real Lie symmetries (RLSs) and complex Lie symmetries (CLSs). The corresponding symmetry counts are related by…