Stability of Nonlinear Normal Modes in the FPU-$\beta$ Chain in the   Thermodynamic Limit
  All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in the thermodynamic limit, as well as its application for each of the above nonlinear normal modes are presented. 
G.M. Chechin, D.S. Ryabov
nlin.PS