Stable and unstable periodic orbits in the one-dimensional lattice ϕ4 theory

Kenichiro Aoki
Phys. Rev. E 94, 042209 – Published 13 October 2016

Abstract

Periodic orbits for the classical ϕ4 theory on the one-dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, free and fixed boundary conditions. Through the process, we investigate which normal modes of the linear theory can or cannot be extended to the full nonlinear theory and why. We then analyze the stability of these orbits, clarifying the link between the stability, parametric resonance, and Lyapunov spectra for these orbits. The construction of the periodic orbits and the stability analysis is applicable to theories governed by Hamiltonians with quadratic intersite potentials and a general on-site potential. We also apply the analysis to theories with on-site potentials that have qualitatively different behavior from the ϕ4 theory, with some concrete examples.

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  • Received 10 June 2016

DOI:https://doi.org/10.1103/PhysRevE.94.042209

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Nonlinear Dynamics

Authors & Affiliations

Kenichiro Aoki*

  • Research and Education Center for Natural Sciences and Hiyoshi Department of Physics, Keio University, Yokohama 223–8521, Japan

  • *ken@phys-h.keio.ac.jp

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Issue

Vol. 94, Iss. 4 — October 2016

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