N-break states in a chain of nonlinear oscillators

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Rodrigues, AS (Author) FCUP; Kevrekidis, PG (Author) Other; Dobson, M (Author) Other

Journal

Title: Physical review. E

Vol. 99

ISSN: 2470-0045

Publisher: American Physical Society

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Q-656

DOI: 10.1103/physreve.99.022201

Abstract (EN): In the present work we explore a prestretched oscillator chain where the nodes interact via a pairwise Lennard-Jones potential. In addition to a homogeneous solution, we identify solutions with one or more (so-called) "breaks," i.e., jumps. As a function of the canonical parameter of the system, namely, the precompression strain d, we find that the most fundamental one-break solution changes stability when the monotonicity of the Hamiltonian changes with d. We provide a proof for this (motivated by numerical computations) observation. This critical point separates stable and unstable segments of the one-break branch of solutions. We find similar branches for two- through five-break branches of solutions. Each of these higher "excited state" solutions possesses an additional unstable pair of eigenvalues. We thus conjecture that k-break solutions will possess at least k - 1 (and at most k) pairs of unstable eigenvalues. Our stability analysis is corroborated by direct numerical computations of the evolutionary dynamics.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10