<p>This study proposes a generic self-similar transformation with an amplitude-matching function to map the inhomogeneous nonlinear Schrödinger equation (INLSE) onto the integrable standard NLSE. By introducing scaling functions that govern beam amplitude, width, and phase, we derive compatibility conditions enabling exact solutions for arbitrary dispersion, external potential, and gain/loss. Inspired by the concept of Darboux transformations, we systematically generate hierarchies of solutions—including bright/dark solitons, Akhmediev breathers, Ma breathers, and rogue waves—through parametric scaling and iterative construction. These solutions are extended to coupled INLSE systems, revealing the interaction dynamics of self-similar waves under exponential dispersion profiles. Our approach provides a unified framework for designing photonic devices, Bose–Einstein condensates, and fiber systems with dispersion management.</p>