Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

Abstract

We investigate non-autonomous solitons in a general coherently coupled nonlinear Schrödinger (CC-NLS) 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.

Engineering optical rogue waves and breathers in a coupled nonlinear Schrödinger system with four-wave mixing effect

“…As a future study, the present investigation shall be extended to general solitons and their collisions with appropriate modulated nonlinearities which is reported recently [38]. Further, one can also study the dynamics of various nonlinear coherent structures, their co-existence and dynamics in dispersion as well as nonlinearity management in various systems, for example [39,40], by incorporating gain/ loss too.…”

Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model

“…However, we can find only a handful amount of works for such variable background nonlinear waves compared to their counterparts on constant backgrounds. In the context of nonlinear optics, the effects of spatially-and temporally-varying backgrounds on solitons, breathers and rogue waves have revealed interesting outcomes that can be useful to understand the influence of nonuniform models [5,46,47]. Similarly, the dynamics of nonlinear waves on controllable backgrounds due to non-autonomous nonlinearities are explored in Bose-Einstein condensates too [6,[48][49][50][51][52].…”

“…The above studies revealed different exciting results such as amplification, compression, bending/snaking, tunnelling/cross-over, superposed structures, etc. [5,6,[46][47][48][49][50][51][52][53][54][55][56][57][58]. So, it is our natural interest to question the possibility of realizing such phenomena in the above mentioned fifth-order nonlinear model (1).…”

Localized waves and interaction solutions to an integrable variable coefficients Jimbo-Miwa equation

“…Hirota bilinear method is a direct and effective method for solving integrable nonlinear PDEs [27][28][29]. The Hirota bilinear method constructs the bilinear form of the original equation by introducing appropriate rational transformations to the potential function of the PDE.…”