Nonlinear tunneling of solitons in a variable coefficients nonlinear Schr\"odinger equation with $\mathcal{PT}$-symmetric Rosen-Morse potential

TL;DR

This paper constructs and analyzes soliton solutions in a variable coefficients nonlinear Schrödinger equation with a $\\mathcal{PT}$-symmetric Rosen-Morse potential, revealing nonlinear tunneling effects influenced by potential barriers and wells.

Contribution

It introduces a similarity transformation method to derive soliton solutions in a $\\mathcal{PT}$-symmetric setting with variable coefficients, exploring nonlinear tunneling phenomena.

Findings

Solitons can tunnel through nonlinear barriers and wells with amplitude modifications.

The soliton behavior depends on the sign of the potential height.

Results are applicable to optical device modeling.

Abstract

We construct soliton solution of a variable coefficients nonlinear Schr\"odinger equation in the presence of parity reflection - time reversal $(\mathcal{PT})-$ symmetric Rosen-Morse potential using similarity transformation technique. We transform the variable coefficients nonlinear Schr\"odinger equation into the nonlinear Schr\"odinger equation with $\mathcal{PT}-$symmetric potential with certain integrability conditions. We investigate in-detail the features of the obtained soliton solutions with two different forms of dispersion parameters. Further, we analyze the nonlinear tunneling effect of soliton profiles by considering two different forms of nonlinear barrier/well and dispersion barrier/well. Our results show that the soliton can tunnel through nonlinear barrier/well and dispersion barrier/well with enlarged and suppressed amplitudes depending on the sign of the height. Our theoretical findings are experimentally realizable and might help to model the optical devices.