1995/09/25 by Sergej Flach, S. Flach · 4 citations
Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Bifurcation #Bifurcation theory #Complex plane #Hamiltonian (control theory) #Hamiltonian system #Nonlinear Photonic Systems #Nonlinear system #Perturbation (astronomy) #Quantum Mechanics and Non-Hermitian Physics #Symmetry breaking #Tangent #nlin.PS #patt-sol
paper · pdf · doi:10.1016/0167-2789(95)00267-7
uuencoded file, uudecoding gives 'bifurcation.tar'. Contents: one LaTeX file (~ 30 pages), four gziped ps files of the figures. Accepted for publication in PHYSICA D
arxiv created 1995/09/25 · openalex publication_date 1996/03/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new bifurcated periodic orbits. The case of two coupled oscillators is considered as an example for the perturbation analysis, where the symmetry breaking can be traced using Poincare maps. Next we consider a lattice and derive the dependence of the bifurcation energy on the parameters of the Hamiltonian function in the limit of large system sizes. A necessary condition for the occurence of the bifurcation is the repelling of the band edge plane wave's frequency from the linear spectrum with increasing energy. We conclude that the bifurcated orbits will consequently exponentially localize in the configurational space.