Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative

Details Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative

2012-02-02

arxiv.org/abs/1202.0356v1

EPL, 97 (2012) 30007

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages, 5 figures

Scientific paper

10.1209/0295-5075/97/30007

In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear Schr\"odinger equation(DNLSE). One novel feature of VCDNLSE with DI is that its coefficients can be designed artificially and analytically by using transformation. What is more, from the rogue wave and rational traveling solution of the DNLSE, we get two kinds of rogue waves of the VCDNLSE by this transformation. One kind of rogue wave has vanishing boundary condition, and the other non-vanishing boundary condition. The DI of the VCDNLSE also provides a possible way to control the profile of the rogue wave in physical experiments.

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