5 problems

Let $(M^n,g)$ be a Riemannian manifold with $n\geq 2$, and write $g=(g_{ij})$ in local coordinates $(x^1,\ldots,x^n)$. Let $t$ denote time, and let $\xi^1,\ldots,\xi^n$ be arbitrar…

Let $\mathcal{C}$ denote the class of two-dimensional shallow water equations, let $G^\sim$ be its equivalence group, and call an admissible transformation independent when it is i…

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…

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…