Compactlike discrete breathers in systems with nonlinear and nonlocal dispersive terms

Abstract

Discrete breathers with purely anharmonic short-range interaction potentials localize super-exponentially becoming compact-like. We analyze their spatial localization properties and their dynamical stability. Several branches of solutions are identified. One of them connects to the well-known Page and Sievers-Takeno lattice modes, another one connects with the compacton solutions of Rosenau. The absence of linear dispersion allows for extremely long-lived time-quasiperiodic localized excitations. Adding long-range anharmonic interactions leads to an extreme case of competition between length scales defining the spatial breather localization. We show that short- and long-range interaction terms competition results in the appearance of several characteristic cross-over lengths and essentially breaks the concept of compactness of the corresponding discrete breathers.

5 pages, 4 figures, revised version, published in PRE

References in corpus (8)

• Discrete Breathers
• Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array
• Experimental Generation and Observation of Intrinsic Localized Spin Wave Modes in an Antiferromagnet
• Conditions on the Existence of Localized Excitations in Nonlinear Discrete Systems
• Optical manipulation of intrinsic localized vibrational energy in cantilever arrays
• Breathers on lattices with long range interaction
• Discrete breathers in Fermi-Pasta-Ulam lattices
• Multi-component structure of nonlinear excitations in systems with length-scale competition

Cited by in corpus (15)

• Review of Some Promising Fractional Physical Models
• Continuous Limit of Discrete Systems with Long-Range Interaction
• Coupled oscillators with power-law interaction and their fractional dynamics analogues
• Map of Discrete System into Continuous
• Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
• Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory
• Application of the GALI Method to Localization Dynamics in Nonlinear Systems
• The Localization Length of Stationary States in the Nonlinear Schreodinger Equation
• The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential
• Dark discrete breather modes in monoaxial chiral helimagnet with easy-plane anisotropy
• Chains with Fractal Dispersion Law
• Boundary effects on the dynamics of chains of coupled oscillators
• Resonant frequencies and spatial correlations in frustrated arrays of Josephson type nonlinear oscillators
• All-phononic Amplification in Coupled Cantilever Arrays based on Gap Soliton Dynamics
• Supratransmission in Lattices with Purely Nonlinear Coupling