Publication Date
2020
Journal or Book Title
Communications in Nonlinear Science and Numerical Simulation
Abstract
We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit. By means of direct simulations, it is found that the instability leads to a breakup of the quasi-1D breather in a chain of interacting 2D radial breathers that appear to be fairly robust in the dynamics. The stability and dynamics of radial breathers in a finite domain are studied in detail by means of numerical methods. Different families of such solutions are identified. They develop small-amplitude spatially oscillating tails (“nanoptera”) through a resonance of higher-order breather’s harmonics with linear modes (“phonons”) belonging to the continuous spectrum. These results demonstrate the ability of the 2D sG model within our finite domain computations to localize energy in long-lived, self-trapped breathing excitations.
DOI
https://doi.org/10.1016/j.cnsns.2020.105596
Volume
94
License
UMass Amherst Open Access Policy
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Kevrekidis, Panayotis G.; Carretero-González, R.; Cuevas-Maraver, J.; Frantzeskakis, D. J.; Caputo, J.-G.; and Malomed, B. A., "Breather stripes and radial breathers of the two-dimensional sine-Gordon equation" (2020). Communications in Nonlinear Science and Numerical Simulation. 1307.
https://doi.org/10.1016/j.cnsns.2020.105596