Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains. (10th July 2015)

• Record Type: Journal Article
• Authors: Herrmann, Michael; Matthies, Karsten
• Is Part Of: Nonlinearity. Volume 28:Number 8(2015:Aug.)
• Page Start: 2767
• Page End: 2789
• Publication Date: 2015-07-10
• Subjects: asymptotic analysis -- lattice waves -- high-energy limit of FPU-type chains; 37K60 -- 37K40 -- 74H10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/8/2767
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an explicit formula for the wave speed. The key step in our approach is the derivation of an asymptotic ODE for the appropriately rescaled strain profile.