Strength amplification of optical waves via an external potential in (3+1)-dimensional cylindrical NLSE: modulated wave gain and nonlinear phase effect

Abstract The (3 + 1) -dimensional cylindrical nonlinear Schrodinger equation (3DCNLSE) governs the propagation of ultrashort optical pulses in cylindrical optical fibers and wave guides. It is extensively employed to model light beams carrying orbital angular momentum (OAM) and plays a central role in the design and optimization of high-speed fiber-optic communication systems. Most existing studies on the 3DCNLSE have primarily relied on numerical simulations or physics-informed neural networks (PINNs), with comparatively limited analytical investigations. In the present work, our main objective is to explore the impact of an external potential (EP) on the strength of optical waves (OWs) by deriving exact solutions of the (3+1)-dimensional cylindrical nonlinear Schrodinger equation (3DCNLSE). More general classes of exact solutions are constructed by introducing a complex amplitude transformation, rather than the real-valued transformations that are commonly employed in the existing literature. Here, the extended unified method is used. From a space– plasma perspective, the external potential can be interpreted as representing the lunar surface, thereby extending the applicability of the model to modulated Langmuir waves propagating in the plasma environment near the Moon. Graphical analysis reveals that the presence of the external potential significantly enhances the amplitude and localization of the optical waves (OWs), which may contribute to improving channel capacity in high-speed communication systems. In addition, the graphs reveal that the OWs exhibit markedly higher strength along the cylindrical axis than within the core, suggesting anisotropic energy localization induced by the cylindrical geometry. This amplification mechanism is therefore of practical relevance for advanced fiber-optic technologies.Moreover, modulation instability (MI) is investigated. It is shown that MI arises when the dispersion and Kerr nonlinearity coefficients possess the same sign. In contrast, the exact solutions derived in this study exist when these coefficients have opposite signs, indicating that the obtained wave structures propagate in a stable regime.The corresponding modulation gain spectrum is also characterized. Finally, the role of the nonlinear phase is clarified. It is demonstrated that phase modulation can induce structural deformations in the cylindrical wave profiles, leading to the formation of localized gaps or slit-like features. These findings provide deeper insight into the interplay between external potentials, nonlinear effects, and stability mechanisms in cylindrical optical and plasma wave dynamics.