Energy criterion for the spectral stability of discrete breathers

Abstract

Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the emergence of instabilities of discrete breathers analogous to the well-established Vakhitov-Kolokolov criterion for solitary waves. The criterion involves the change of monotonicity of the discrete breather's energy as a function of the breather frequency. Our analysis suggests and numerical results corroborate that breathers with increasing (decreasing) energy-frequency dependence are generically unstable in soft (hard) nonlinear potentials.

5 pages, 3 figures. Includes Supplementary Material

References in corpus (2)

• Bright and dark breathers in Fermi-Pasta-Ulam lattices
• Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Cited by in corpus (14)

• Nonlinear Coherent Structures in Granular Crystals
• A Unifying Perspective: Solitary Traveling Waves As Discrete Breathers And Energy Criteria For Their Stability
• Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators
• Breather stripes and radial breathers of the two-dimensional sine-Gordon equation
• An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices
• Discrete breathers in a mechanical metamaterial
• Some breathers and multi-breathers for FPU-type chains
• A general multi-wave quasi-resonance theory for lattice energy diffusion
• Discrete breathers in ${\varphi }^4$ and related models
• Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
• Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
• N-break states in a chain of nonlinear oscillators
• Moving discrete breathers in a $\beta$-FPU lattice revisited
• Unstable dynamics of solitary traveling waves in a lattice with long-range interactions