5 problems

Consider a diatomic Fermi–Pasta–Ulam system in a singular limit whose center manifold remains two-dimensional, while its stable and unstable manifolds are infinite-dimensional. Hom…

Let $appa$ be the small-amplitude parameter and let $igma$ be the wave-speed parameter. Fixing either $appa$ or $igma$ produces one-dimensional cross-sections of the traveling-wave…

Let $\epsilon>0$ be the near-sonic small-amplitude parameter, let $c_{\epsilon}$ be the corresponding wave speed, and let $K_{c_{\epsilon}}$ denote the leading-order coefficient of…

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…

The Fermi–Pasta–Ulam chain has $N$ identical masses connected by nonlinear springs, with the elastic force expanded as … The original $\alpha$-FPU system is the case $\alpha\ne0$ a…