Open AccessSecond-order rogue wave breathers in the nonlinear Schrödinger equation with quadratic potential modulated by a spatially-varying diffraction coefficient
Author(s) -
WeiPing Zhong,
Milivoj R. Belić,
Yiqi Zhang
Publication year - 2015
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.23.003708
Subject(s) - rogue wave , breather , quadratic equation , nonlinear schrödinger equation , matrix similarity , physics , diffraction , nonlinear system , modulation (music) , transformation (genetics) , modal , schrödinger equation , quantum mechanics , classical mechanics , mathematical analysis , mathematics , partial differential equation , geometry , materials science , biochemistry , chemistry , acoustics , polymer chemistry , gene
Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.