Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schr\"odinger models with variable nonlinearities

TL;DR

This paper studies non-autonomous vector solitons in inhomogeneous nonlinear Schrödinger systems with variable nonlinearities and external potentials, revealing complex modulated solitonic behaviors and collision transformations.

Contribution

It introduces a generalized similarity transformation and exact soliton solutions for a broad class of inhomogeneous CCNLS systems, advancing understanding of soliton dynamics under variable nonlinearities.

Findings

Identified a transformation linking inhomogeneous and homogeneous CCNLS models.

Discovered modulated solitonic phenomena such as oscillation, amplification, and tunneling.

Showed how inhomogeneous nonlinearities can alter soliton collision outcomes.

Abstract

We investigate non-autonomous solitons in a general coherently coupled nonlinear Schr\"odinger (CCNLS) system with temporally modulated nonlinearities and with an external harmonic oscillator potential. This general CCNLS system encompasses three distinct types of CCNLS equations that describe the dynamics of beam propagation in an inhomogeneous Kerr-like nonlinear optical medium for different choices of nonlinear polarizations owing to the anisotropy of the medium. We identify a generalized similarity transformation to relate the considered model into the standard integrable homogeneous coupled nonlinear evolution equations with constant nonlinearities, accompanied by a constraint relation expressed in the form of the Riccati equation. With the help of a non-standard Hirota's bilinearization method and exact soliton solutions, we explore the impact of varying nonlinearities and refractive index in the propagation and collisions analytically by reverse engineering. Interestingly, we show the emergence of several modulated solitonic phenomena such as periodic oscillation, amplification, compression, tunneling/cross-over, excitons, as well as their combined effect in the single-soliton propagation and two-soliton collisions with appropriate forms of nonlinearity. Notably, we identify a tool to transform the nature of soliton collisions with certain type of inhomogeneous nonlinearities. The results could be of significant interest to the studies on management of nonlinear waves in the contexts like nonlinear optics and can also be extended to Bose-Einstein condensates and super-fluids.