期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 47, 期 45, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/47/45/455101
关键词
PT-symmetry; breathers; sine-Gordon
资金
- National Science Foundation [CMMI-1000337, DMS-1312856]
- Binational Science Foundation [2010239]
- FP7-People [IRSES-606096]
- US-AFOSR [FA9550-12-10332]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1312856] Funding Source: National Science Foundation
In this work, we explore a prototypical example of a genuine continuum breather (i.e., not a standing wave) and the conditions under which it can persist in a PT-symmetric medium. As our model of interest, we will explore the sine-Gordon equation in the presence of a PT-symmetric perturbation. Our main finding is that the breather of the sine-Gordon model will only persist at the interface between gain and loss that PT-symmetry imposes but will not be preserved if centered at the lossy or at the gain side. The latter dynamics is found to be interesting in its own right giving rise to kink-antikink pairs on the gain side and complete decay of the breather on the lossy side. Lastly, the stability of the breathers centered at the interface is studied. As may be anticipated on the basis of their 'delicate' existence properties such breathers are found to be destabilized through a Hopf bifurcation in the corresponding Floquet
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