We present a detailed numerical and analytical study of the stability properties of the pi/2-mode nonlinear solution of the Fermi-Pasta-Ulam- system. The numerical analysis is made as a function of the number N of the particles of the system and of the product epsilon*beta, where epsilon is the energy density and beta is the parameter characterizing the nonlinearity. It is shown that, both for beta>0 and beta>0, the instability threshold value converges, with increasing N, to the same value , that for beta>0 it is a decreasing function of N as in the pi -mode, whereas, for beta< 0, it is an increasing one. The asymptotic behavior of the threshold value for large values of N is analytically obtained in both cases with a Floquet analysis of the stability.
Stability properties of the N/4 (pi/2-mode) one-mode nonlinear solution of the Fermi-Pasta-Ulam- beta system
LEO, Mario;
2007-01-01
Abstract
We present a detailed numerical and analytical study of the stability properties of the pi/2-mode nonlinear solution of the Fermi-Pasta-Ulam- system. The numerical analysis is made as a function of the number N of the particles of the system and of the product epsilon*beta, where epsilon is the energy density and beta is the parameter characterizing the nonlinearity. It is shown that, both for beta>0 and beta>0, the instability threshold value converges, with increasing N, to the same value , that for beta>0 it is a decreasing function of N as in the pi -mode, whereas, for beta< 0, it is an increasing one. The asymptotic behavior of the threshold value for large values of N is analytically obtained in both cases with a Floquet analysis of the stability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
