Author(s)

Haoqi Zhou¹, Shuwei Xu^1*, Maohua Li²

¹College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, China.
²School of Mathematics and Statistics, Ningbo University, Ningbo, China.

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).

Derivative Nonlinear Schrödinger Equation, Breather Solution, Phase Solution, Soliton-Like Solutions, Peregrine Rogue Waves, Darboux Transformation

Zhou, H. , Xu, S. and Li, M. (2020) Peregrine Rogue Waves Generated by the Interaction and Degeneration of Soliton-Like Solutions: Derivative Nonlinear Schrödinger Equation. Journal of Applied Mathematics and Physics, 8, 2824-2835. doi: 10.4236/jamp.2020.812208.