Micropterons, nanopterons and solitary wave solutions to the diatomic Fermi–Pasta–Ulam–Tsingou problem

Partial Differential Equations in Applied Mathematics

Hermen Jan Hupkes¹  Timothy E. Faver² 

[1] Corresponding author.;Department of Mathematics, Kennesaw State University, 850 Polytechnic Lane, MD 9085, Marietta, GA 30060, United States of America;

关键词: FPU;    FPUT;    Diatomic lattice;    Heterogeneous granular media;    Nanopteron;    Micropteron;   

DOI  :  

来源: DOAJ

【 摘 要 】

We use a specialized boundary-value problem solver for mixed-type functional differential equations to numerically examine the landscape of traveling wave solutions to the diatomic Fermi–Pasta–Ulam–Tsingou (FPUT) problem. By using a continuation approach, we are able to uncover the relationship between the branches of micropterons and nanopterons that have been rigorously constructed recently in various limiting regimes. We show that the associated surfaces are connected together in a nontrivial fashion and illustrate the key role that solitary waves play in the branch points. Finally, we numerically show that the diatomic solitary waves are stable under the full dynamics of the FPUT system.

【 授权许可】

Unknown