Moving discrete breathers in nonlinear lattice: Resonance and stability

We have studied moving discrete breathers in the Fermi–Pasta–Ulam β lattice. The moving discrete breathers are not strictly localized but have spatially extended tails. It is shown that a resonance phenomenon in the tail amplitude occurs: the tail amplitude is enhanced for some particular values of the breather frequency and these values depend on the velocity. This resonance is caused by strong excitation of a particular set of the harmonic normal modes. We analytically derive a condition for this resonance. Moreover, we analyze the linear stability of moving discrete breathers and show that the instability appears when the breather frequency is close to the resonance points.