Eur. Phys. J. Plus (2015) 130: 199
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

Abstract

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.