Self-similar rogue waves and nonlinear tunneling effects in inhomogeneous nonlinear fiber optics

Abstract

Analytical first- and second-order rogue wave solutions of the inhomogeneous modified nonlinear Schrödinger equation are presented by using similarity transformation. Then, by the proper choices of the inhomogeneous coefficients and free parameters, the controllable behaviors of the optical rogue waves are graphically discussed in the nonlinear fiber optics context. It is found that the width of the rogue wave can be tuned by adjusting the parameter $k$ and the locations of the rogue waves are linearly controlled by the parameter $\mathit{\lambda }$. The intensities of the rogue waves are influenced by the inhomogeneous linear gain/loss coefficient $p(z)$ and parameter $A_0$. The dispersion management function $f(z)$ has effects on the periods and trajectories of the rogue waves and can induce maintenance (or annihilation) along $z$ direction. Interestingly, the composite rogue waves are revealed, the location of which is manipulated through changing the dispersion management function $f(z)$. Additionally, the nonlinear tunneling of those rogue waves is investigated as they propagate through a dispersion barrier (or well) and nonlinear barrier (or well).

Keywords:

• inhomogeneous modified nonlinear Schrödinger equation
• location manipulation
• rogue wave compression
• intensity manipulation
• rogue wave maintenance and annihilation
• composite rogue wave
• trajectory manipulation
• nonlinear tunneling

Acknowledgements

We express our sincere thanks to the Editors, Referees and all the members of our discussion group for their valuable comments.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11226193], [grant number 11247292], [grant number 11305060]; by the Postdoctoral Science Foundation of China [grant number 2013M540907], [grant number 2014T70061]; by the Key Project of Fundamental Research Funds of the Central Universities [grant number 2015ZD16]; by the Innovative Talents Scheme of North China Electric Power University.