Localized structures on librational and rotational travelling waves in the sine-Gordon equation
arXiv:2006.09944 · doi:10.1098/rspa.2020.0490
Abstract
We derive exact solutions to the sine--Gordon equation describing localized structures on the background of librational and rotational travelling waves. In the case of librational waves, the exact solution represents a localized spike in space-time coordinates (a rogue wave) which decays to the periodic background algebraically fast. In the case of rotational waves, the exact solution represents a kink propagating on the periodic background and decaying algebraically in the transverse direction to its propagation. These solutions model the universal patterns in the dynamics of fluxon condensates in the semi-classical limit. The different dynamics is related to different outcomes of modulational stability of the librational and rotational waves.
arXiv comment22 pages; 8 figures
References in corpus (7)
- Multi-breathers and high order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
- Rogue periodic waves of the mKdV equation
- Rogue periodic waves of the focusing NLS equation
- Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background
- Rogue waves on the double-periodic background in the focusing nonlinear Schrodinger equation
- On the stability analysis of periodic sine-Gordon traveling waves
- The Stability Spectrum for Elliptic Solutions to the Sine-Gordon Equation
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