The stability properties of certain simple periodic solutions (nonlinear modes) of the equations of motion of one-dimensional, N-particle FPU lattices, are obtained analytically by uncoupling the N linear variational equations. The energy per particle Ec/N at which these modes first become unstable is calculated and its asymptotic behavior as N→∞ is determined. We find that for lattices which experience strong energy sharing Ec/N →0 as N →∞, while for a lattice where little energy sharing is observed Ec/N →const > 0, as N increases. Certain possible connections between our local stability results and some global chaotic properties of FPU lattices are discussed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics