Dispersion management and optical soliton engineering in nonuniform inhomogeneous PT-symmetric nonlinear media

Studies on optical solitons in inhomogeneous media continue to attract immense interest. This work is devoted to exploring the evolution dynamics of solitons in inhomogeneous nonuniform optical media with parity-time reversal $\left(\mathrm{PT}\right)$-symmetric rational potential and variable dispersion through explicit solutions. For this purpose, we consider a variable-coefficient nonlinear Schrödinger (vcNLS) equation containing $\mathrm{PT}$-symmetric rational potential consisting of constant nonlinearity and longitudinally-varying dispersion and tapering effects. By implementing a similarity transformation, one of the efficient methods to analyze variable-coefficient (non-autonomous) nonlinear models, we construct explicit soliton (similariton) solutions and investigate deformations occurring in the characteristics of the optical solitons resulting from various dispersion modulations. Notably, we unravel the dynamical changes in the amplitude, width, shape, speed/velocity, and localization of solitons for periodic, localized well/barrier-type, and step-like dispersion modulations leading to periodic, localized, and single-step suppression or amplification, broadening and narrowing of width, and advancing or delaying the transitions during soliton propagation in inhomogeneous media. Besides, we execute a direct numerical experiment to validate the identified analytical findings. The observed results shall enhance the understanding of solitons in inhomogeneous $\mathrm{PT}$-symmetric media. As future perspectives, the present analysis can be extended to study the deformation dynamics of several other nonlinear waves in inhomogeneous media and their experimental realizations in the context of optics and other fields.