Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices

Nonlinear Sciences – Pattern Formation and Solitons

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

23 pages, 1 figure

Scientific paper

10.1016/j.physd.2005.04.006

In {\em Physica D} {\bf 91}, 223 (1996), results were obtained regarding the tangent bifurcation of the band edge modes ($q=0,\pi$) of nonlinear Hamiltonian lattices made of $N$ coupled oscillators. Introducing the concept of {\em partial isochronism} which characterises the way the frequency of a mode, $\omega$, depends on its energy, $\epsilon$, we generalize these results and show how the bifurcation energies of these modes are intimately connected to their degree of isochronism. In particular we prove that in a lattice of coupled purely isochronous oscillators ($\omega(\epsilon)$ strictly constant), the in-phase mode ($q=0$) never undergoes a tangent bifurcation whereas the out-of-phase mode ($q=\pi$) does, provided the strength of the nonlinearity in the coupling is sufficient. We derive a discrete nonlinear Schr\"odinger equation governing the slow modulations of small-amplitude band edge modes and show that its nonlinear exponent is proportional to the degree of isochronism of the corresponding orbits. This equation may be seen as a link between the tangent bifurcation of band edge modes and the possible emergence of localized modes such as discrete breathers.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-87683

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.