Localized structures on librational and rotational travelling waves in the sine-Gordon equation
Localized structures on librational and rotational travelling waves in the sine-Gordon equation
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 …