On the characterization of breather and rogue wave solutions of an inhomogeneous nonlinear Schr\"odinger equation

TL;DR

This paper derives and analyzes breather and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation with an external potential, revealing how inhomogeneity affects wave shape and trajectories in plasma media.

Contribution

It introduces new localized solutions for a variable coefficient nonlinear Schrödinger equation, accounting for inhomogeneity and external potential effects.

Findings

Inhomogeneity alters wave shape and orientation.

Derived multiple localized solutions including Ma and Akhmediev breathers.

Showed trajectories of rogue waves in inhomogeneous media.

Abstract

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium. We derive several localized solutions including Ma breather, Akhmediev breather, two-breather and rogue wave solutions of this model and show how the inhomogeneity of space modifies the shape and orientation of these localized structures. We also depict the trajectories of the inhomogeneous rogue wave. Our results may be useful for controlling plasmonic energy along the plasma surface.