title: Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation.
abstract: We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schrödinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
authors.affiliation: School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China.
authors.forename: Yunqing
authors.initials: Y
authors.lastname: Yang
authors.affiliation: Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Zhenya
authors.initials: Z
authors.lastname: Yan
authors.affiliation: Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv 59978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed