Solitary waves in FPU-type lattices

Discrete breathers in a mechanical metamaterial

“…( 2) for each frequency ω, to represent the bifurcation diagrams. Similar to the case of solitary waves [53], energy is an intrinsic characteristic of DBs, and thus represents a natural choice of a dependent variable. Importantly, change in monotonicity of the energy-frequency curve has been linked with a potential change in breather stability [47], a feature that will also be encountered in what follows.…”

KP-II approximation for a scalar FPU system on a 2D square lattice

“…The leading-order energy E 0 in (25) suggests that the energy estimates for the system (20) and ( 21) are obtained by multiplying the first equation by the weighted time derivative ω −2 k ∂ t R u and the second equation by the weighted time derivative ω −2 l ∂ t R v , after which we add the two equations and integrate in = (k, l). This procedure gives us the following energy balance equation…”

“…These terms give the time derivative of the third and fourth terms in the leading-order energy E 0 in (25).…”

“…Applications of these methods for other generalized KdV equations can be found in [5,11,13,15]. Properties of solitary waves in the FPU system in one spatial dimension were recently reviewed in [25].…”

Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples

“…A polyatomic, or polymer, Fermi–Pasta–Ulam–Tsingou (FPUT) lattice 1–5 is an infinite, one‐dimensional chain of particles, connected on the left and right to their nearest neighbors by springs, with motion constrained to a horizontal axis. We index the particles and springs by integers $$j \in \mathbb {Z}$$; the j th spring connects the j th particle on the left to the $$(j+1)$$st particle on the right.…”