TITLE:
Peregrine Rogue Waves Generated by the Interaction and Degeneration of Soliton-Like Solutions: Derivative Nonlinear Schrödinger Equation
AUTHORS:
Haoqi Zhou, Shuwei Xu, Maohua Li
KEYWORDS:
Derivative Nonlinear Schrödinger Equation, Breather Solution, Phase Solution, Soliton-Like Solutions, Peregrine Rogue Waves, Darboux Transformation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.12,
December
15,
2020
ABSTRACT: We study the Peregrine rogue waves within the framework of Derivative Nonlinear Schrödinger equation, which is used to describe the propagation of Alfven waves in plasma physics and sub-picosecond or femtosecond pulses in nonlinear optics. The interaction and degeneration of two soliton-like solutions and its relations for the breather solution have been analyzed. The Peregrine rogue waves have been considered from the two kinds of formation processes: it can be generated through the limitation of the infinitely large period of the breather solutions, and it can be interpreted as the soliton-like solutions with different polarities. As a special example, a special Peregrine rogue wave is generated by a breather solution and phase solution, which is given by the trivial seed (zero solution).