Multibreathers in Klein-Gordon chains with interactions beyond nearest neighbors

Abstract

We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for arbitrarily varying (as a function of the node distance) linear couplings between arbitrary sets of neighbors in the chain. By examining special case examples such as three-site breathers with next-nearest-neighbors, we find {\it crucial} modifications to the nearest-neighbor picture of one-dimensional oscillators being excited either in- or anti-phase. Configurations with nontrivial phase profiles, arise, as well as spontaneous symmetry breaking (pitchfork) bifurcations, when these states emerge from (or collide with) the ones with standard (0 or $\pi$) phase difference profiles. Similar bifurcations, both of the supercritical and of the subcritical type emerge when examining four-site breathers with either next-nearest-neighbor or even interactions with the three-nearest one-dimensional neighbors. The latter setting can be thought of as a prototype for the two-dimensional building block, namely a square of lattice nodes, which is also examined. Our analytical predictions are found to be in very good agreement with numerical results.

References in corpus (4)

• The Discrete Nonlinear Schrödinger equation - 20 Years on
• Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations
• Moving breathers in bent DNA with realistic parameters
• Effect of the Introduction of Impurities on the Stability Properties of Multibreathers at Low Coupling

Cited by in corpus (9)

• Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic symmetry
• Nonlinear Excitations in Magnetic Lattices with Long-Range Interactions
• On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice
• An extensive resonant normal form for an arbitrary large Klein-Gordon model
• The Drastic Role of Beyond Nearest-Neighbor Interactions on Two-Dimensional Dynamical Lattices: A Case Example
• On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori
• Discrete breathers in ${\varphi }^4$ and related models
• On the nonexistence of degenerate phase-shift multibreathers in a zigzag Klein-Gordon model
• Long time stability of small amplitude Breathers in a mixed FPU-KG model