2009/01/23 by Michael Herrmann · 38 citations
Materials Science · Mathematics · Physics and Astronomy · #Chain (unit) #Computation #Energy (signal processing) #Homoclinic orbit #Maximization #Nonlinear Photonic Systems #Organic and Molecular Conductors Research #Regular polygon #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:37K60 #msc:47J30 #msc:70F45 #msc:74J30
paper · pdf · doi:10.1017/s0308210509000146
published in Proceedings of the Royal Society of Edinburgh Section A Mathematics 140(4), 753-785 (Cambridge University Press) · 27 pages, several figures
arxiv created 2009/01/23 · openalex publication_date 2010/08/01 · arxiv updated 2010/08/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider atomic chains with nearest neighbour interactions and study periodic travelling waves and homoclinic travelling waves, which are called wavetrains and solitons, respectively. Our main result is a new existence proof which relies on the constrained maximization of the potential energy and exploits the invariance properties of an improvement operator. The approach is restricted to convex interaction potentials but refines the standard results, as it provides the existence of travelling waves with unimodal and even profile functions. Moreover, we discuss both the numerical approximation and the complete localization of wavetrains, and show that wavetrains converge to solitons when the periodicity length tends to infinity.