Journal
NONLINEAR DYNAMICS
Volume 96, Issue 4, Pages 2535-2546Publisher
SPRINGER
DOI: 10.1007/s11071-019-04939-1
Keywords
Geophysical flows; Non-autonomous generalized AB system; Solitary and rogue waves; Controllable backgrounds
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Funding
- Science Research Project of Higher Education in Inner Mongolia Autonomous Region [NJZZ18117]
- Natural Science Foundation of Inner Mongolia Autonomous Region [2018BS01004]
- China Postdoctoral Science Foundation [2018M640094]
- Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region [NJYT-19-B21]
- National Natural Science Foundation of China [11772017]
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Investigated in this paper is a non-autonomous generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows. We discover that the two short waves and mean flow can evolve in the forms of the multi-rogue waves on the condition that the nonlinearity effect sigma is positive. Via the Darboux and generalized Darboux transformations, we obtain the first- and second-order rogue waves as well as the algorithm to derive the Nth-order rogue waves. It is revealed that the perturbation function (t) has no effect on the two short waves while affects the mean flow by changing its evolution background. When sigma is negative, those rogue waves turn to be singular. In addition, we find that the two short waves and mean flow can also appear as the solitary waves, and they perform as the bright solitons under sigma>0 while perform as the dark solitons under sigma<0. With the Hirota method, introducing the auxiliary function (t), we derive the first- and second-order bright and dark solitary waves. Both solitary wave velocities are related to (t) and (t). Besides, (t) and (t) have no effect on the amplitudes of the two short waves but bring about controllable backgrounds and deformations of the solitary waves for the mean flow.
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