https://doi.org/10.1140/epjp/i2015-15199-8
Regular Article
Semirational solutions and baseband modulational instability of the AB system in fluid mechanics
1
Department of Mathematics and Physics, North China Electric Power University, 102206, Beijing, China
2
School of Electrical and Electronic Engineering, North China Electric Power University, 102206, Beijing, China
3
School of Nuclear Science and Engineering, North China Electric Power University, 102206, Beijing, China
4
School of Information, Beijing Wuzi University, 101149, Beijing, China
5
School of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, China
* e-mail: 50901924@ncepu.edu.cn
Received:
6
August
2015
Revised:
7
September
2015
Accepted:
8
September
2015
Published online:
12
October
2015
Under investigation in this paper is the AB system describing marginally unstable baroclinic wave packets in geophysical fluids. By means of the n -fold modified Darboux transformation, the semirational solutions in terms of the determinants of the AB system are derived. These solutions, which are a combination of rational and exponential functions, can be used to model the nonlinear superposition of the Akhmediev breathers (or the Kuznetsov-Ma breathers) and the rogue waves. The k -order rogue wave of the AB system is produced by the interaction between the l-order rogue wave with 
neighboring elements in the 
-order breathers 
. The proper values of eigenvalue 
and shift 
are also the requirement for generating the higher-order rogue waves. The link between the baseband modulational instability and the existence condition of these rogue waves is revealed.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2015
