5 problems

Let $\psi_t$ be the random field obtained by evolving random initial data under the discrete nonlinear Schrödinger equation, and let $\lambda\neq 0$ be the nonlinearity parameter.…

Weinstein's small-data decay conjecture. Solutions with sufficiently small initial conditions satisfy

Local-uniqueness conjecture. The $2^d$ solutions are locally unique for each $\sigma$ up to lattice translations: $J^{\alpha,\sigma}$ must be centered about $\sigma+M$ for some…

Exponential-smallness conjecture. The Peierls–Nabarro barrier quantities obey

Equivalence conjecture. The optimization problems … have the same solution.