Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio

PHYSICA D-NONLINEAR PHENOMENA

卷:358

Article

Hoffman, Aaron²  Wright, J. Douglas¹ 

[1] Drexel Univ, Philadelphia, PA 19104 USA

[2] Olin Coll Engn, Needham, MA USA

关键词: FPU;    Nanopterons;    Traveling waves;    Solitons;    Singular perturbations;   

DOI  :  10.1016/j.physd.2017.07.004

来源: Elsevier

【 摘 要 】

Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size. In particular we address the limit where the mass ratio tends to zero. The problem is inherently singular and we find that the traveling waves are not true solitary waves but rather nanopterons, which is to say, waves which are asymptotic at spatial infinity to very small amplitude periodic waves. Moreover, we can only find solutions when the mass ratio lies in a certain open set. The difficulties in the problem all revolve around understanding Jost solutions of a nonlocal Schrodinger operator in its semi-classical limit. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free