Stability properties of the N/4 (pi/2-mode) one-mode nonlinear solution of the Fermi-Pasta-Ulam-beta system.
We present a detailed numerical and analytical study of the stability properties of the N/4 (pi/2-mode) one-mode nonlinear solution of the Fermi-Pasta-Ulam-beta system. The numerical analysis is made as a function of the number N of the particles of the system and of the product lambda=epsilonbeta , 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 |lambda(t)(N)| converges, with increasing N , to the same value 2pi(2)(3N(2)) , that for beta>0 |lambda(t)N(2)| is a decreasing function of N as in the pi-mode, whereas, for beta<0 , it is an increasing one. The asymptotic behavior of |lambda(t)| for large values of N is analytically obtained in both cases with a Floquet analysis of the stability.
Dipartimento di Fisica dell'Università del Salento, 73100 Lecce, Italy.
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Leo