Solitary waves in a non-integrable FPU chain

Solitary waves in lattices, represented by homoclinic traveling wave trajectories of discrete dynamical systems, play a crucial role in many areas of science from condensed matter theory to biophysics [1]. In integrable systems solitary waves, known as solitons or quasiparticles, are understood rather thoroughly, with Toda lattice being the most prominent example that covers the whole range of possible behaviors from weak quasicontinuum (QC) waves in almost harmonic chains, to strong anticontinuum (AC) waves in chains of rigid disks [2]. However, quasiparticles in integrable systems do not interact during collisions, which excludes, for instance, finite thermal conductivity. Therefore integrable systems cannot be used as a generic description of localized excitations, and the challenge is to find a non-integrable equivalent of the Toda lattice allowing one to capture a similarly broad range of behaviors.