2017/10/19 by Timothy E. Faver, Faver, Timothy E. · 1 citation
Physics and Astronomy · #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.1710.07376
openalex publication_date 2017/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the existence of traveling waves in a spring dimer\nFermi-Pasta-Ulam-Tsingou (FPUT) lattice. This is a one-dimensional lattice of\nidentical particles connected by alternating nonlinear springs. Following the\nwork of Faver and Wright on the mass dimer, or diatomic, lattice, we find that\nthe lattice equations in the long wave regime are singularly perturbed and\napply a method of Beale to produce nanopteron traveling waves with wave speed\nslightly greater than the lattice's speed of sound. The nanopteron wave\nprofiles are the superposition of an exponentially decaying term (which itself\nis a small perturbation of a KdV sech2-type soliton) and a periodic term of\nvery small amplitude. Generalizing our work in the diatomic case, we allow the\nnonlinearity in the spring forces to have the more complicated form "quadratic\nplus higher order terms." This necessitates the use of composition operators to\nphrase the long wave problem, and these operators require delicate estimates\ndue to the characteristic superposition of function types from Beale's ansatz.\nUnlike the diatomic case, the value of the leading order term in the traveling\nwave profiles alternates between particle sites, so that the spring dimer\ntraveling waves are also "stegotons," in the terminology of LeVeque and Yong.\nThis behavior is absent in the mass dimer and confirms the approximation\nresults of Gaison, Moskow, Wright, and Zhang for the spring dimer.\n