Modulational instability, nonautonomous breathers and rogue waves for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas

Under investigation in this paper is a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation modeling the nonlinear Alfvén waves in the inhomogeneous plasmas. The modulation instability is examined for this inhomogeneous nonlinear model. The nonautonomous breather and rogue wave s...

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Bibliographic Details
Published in:Physics of plasmas 2015-03, Vol.22 (3)
Main Authors: Wang, Lei, Li, Min, Qi, Feng-Hua, Xu, Tao
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
AMPLITUDES
Breathers
Density
INHOMOGENEOUS PLASMA
Longitudinal waves
MAGNETIC FIELDS
Magnetohydrodynamics
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
Nonuniform magnetic fields
PLASMA INSTABILITY
Plasma physics
Plasmas (physics)
Schrodinger equation
SCHROEDINGER EQUATION
Stability
Talbot effect
TUNNEL EFFECT
Variation
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Summary:Under investigation in this paper is a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation modeling the nonlinear Alfvén waves in the inhomogeneous plasmas. The modulation instability is examined for this inhomogeneous nonlinear model. The nonautonomous breather and rogue wave solutions of the vc-DNLS equation are obtained via the modified Darboux transformation. It is found that the velocity and amplitude of the breather can be controlled by the inhomogeneous magnetic field and nonuniform density. Such novel phenomena as breather amplification and nonlinear Talbot effect-like property are demonstrated with the proper choices of the inhomogeneous parameters. Furthermore, dynamics of the fundamental rogue wave, periodical rogue wave, and composite rogue wave are graphically discussed. The trajectories and amplitudes of the rogue waves can be manipulated by the inhomogeneous magnetic field and nonuniform density. In addition, the nonlinear tunneling of the rogue waves and breathers is studied. As an application, a sample model is treated with our results, and the graphical illustrations exhibit the compressing, expanding, and fluctuating phenomena of the Alfvén rogue waves.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.4915516