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).
Highlights
In the past years, rogue waves, commonly defined as gigantic waves appearing from nowhere and disappearing without trace, have attracted a lot of attention in deep ocean waves [1], optical fibers [2] [3], and water tanks [4] [5]
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 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
Summary
Rogue waves, commonly defined as gigantic waves appearing from nowhere and disappearing without trace, have attracted a lot of attention in deep ocean waves [1], optical fibers [2] [3], and water tanks [4] [5]. Considering the generalization of the type of NLS equation, the study of rogue waves in the Derivative Nonlinear Schrödinger(DNLS) equation has caused a lot of research [13] [14] [15] [16] [17]. By introducing an affine parameter, Chen and Lam [28] revised the inverse scattering transform for the DNLS equation under nonvanishing boundary conditions, and got the single breather solution, which can be reduced to the dark soliton and the bright soliton. Based on the explicit expression and their formation process, we can get the relations between breather solutions, phase solutions, soliton solutions and Peregrine rogue waves.
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