8 problems

A diatomic FPUT lattice has a mass ratio, denoted by $\mu$, and a one-sided nanopteron is a travelling wave with an oscillatory tail on only one side of its central leading wave. G…

Consider the macroscopic wave-equation approximation for a lattice with i.i.d. random masses, and denote by a.e.d. and a.e.v. the absolute error measures used in the source. Three-…

Let $c3$ be the small positive parameter appearing in the error estimates, and let $c7$ be the cut-off corrector whose equation is denoted by … . This is a tentative expectation ra…

Soliton resolution conjecture. Asymptotically, the $(n,t)$-space splits into regions separated by straight lines through the origin. Some regions are periodic, with period equal to…

Let $m$ denote the mass ratio in the diatomic lattice. Solitary-wave mass-ratio conjecture. Solitary waves exist for a countable, discrete set of mass ratios $m$ accumulating at…

Periodicity and escape conjecture. If $\overline{\alpha}$ is odd, then all orbits of $\mathcal{F}$ are periodic, and for all but finitely many initial conditions, their period unde…

In a one-dimensional lattice model, let momentum be conserved and consider the long-time, large-scale transport of energy. Momentum-conservation superdiffusivity conjecture. Moment…

Let the lattice directions be represented by the coordinate vectors $(1,0)$ and $(0,1)$, and consider planar travelling fronts together with a large class of initial data for the l…