Breather stripes and radial breathers of the two-dimensional sine-Gordon equation

P. G. Kevrekidis, R. Carretero-González*, J. Cuevas-Maraver, D. J. Frantzeskakis, J. G. Caputo, B. A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Article number105596
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Mar 2021


FundersFunder number
US National Science Foundation
National Science FoundationDMS-1809074, PHY-1602994
National Science Foundation
Directorate for Mathematical and Physical Sciences1809074
Directorate for Mathematical and Physical Sciences
Albert Ellis Institute
Leverhulme TrustP18-RT-3480, PHY-1603058
Leverhulme Trust
European CommissionPID2019-110430GB-C21
European Commission
Israel Science Foundation1286/17
Israel Science Foundation
Ministerio de Ciencia e Innovación


    • Breathers
    • Modulational instabiity
    • Nolinear waves
    • sG equation


    Dive into the research topics of 'Breather stripes and radial breathers of the two-dimensional sine-Gordon equation'. Together they form a unique fingerprint.

    Cite this