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Invited Review Paper: Modulation Instability and Wave Dynamics in Inhomogeneous Nonlinear Optics: A Comprehensive Review
S. Saravana Veni, M.S. Mani Rajan, Yakup Yildirim and Anjan Biswas
This review presents a comprehensive analysis of modulation instability and nonlinear wave dynamics in inhomogeneous nonlinear optical systems, with a focus on the intricate behavior of solitons governed by variable-coefficient and non-isospectral extensions of the higher-order Nonlinear Schrödinger (NLS) equation. Utilizing the Darboux transformation technique grounded on carefully constructed Lax pairs, we survey the exact analytical construction of two- and three-soliton solutions, highlighting novel switching behaviors in the attosecond regime through inelastic soliton interactions. The influence of inhomogeneous coefficients and external potentials on soliton propagation, interaction dynamics, and ring-type structures is systematically investigated. Special attention is given to the role of non-isospectral parameters in shaping complex waveforms, including the emergence of bright-to-dark ring transformations and dromion structures—reported here for the first time. Graphical illustrations and linear stability analysis elucidate the interplay between nonlinearity, dispersion, and inhomogeneity, revealing critical insights into the gain spectrum and soliton stability under varying parameter regimes. Additionally, the interactional behavior of nonautonomous solitons in variable-coefficient optical fibers is explored, with implications for the design of optical logic gates and soliton-based switching devices. The results reviewed in this work not only deepen our understanding of nonlinear wave phenomena in inhomogeneous media but also point toward potential experimental realizations in ultrafast optical communication and soliton management in photonic systems.
Keywords: Solitons, Lax pair, AKNS, Darboux, modulational instability