Optical Solitons and Modulation Instability Analysis with Lakshmanan–Porsezian–Daniel Model Having Parabolic Law of Self-Phase Modulation

This paper seeks to find optical soliton solutions for Lakshmanan–Porsezian–Daniel (LPD) model with the parabolic law of nonlinearity. The spatiotemporal dispersion is included model, as it can contribute handling problem internet bottleneck. study was performed analytically using traveling wave hypothesis reduce an integrable form. Then, resulting equation handled two approaches, namely, auxiliary method and Bernoulli subordinary differential (sub-ODE) method. With intentional focus on hyperbolic function solutions, abundant waves including W-shaped, bright, dark, kink-dark, singular, kink, antikink solitons were derived existing conditions. Furthermore, behaviors some are illustrated. found significantly affect pulse propagation dynamics. Finally, modulation instability (MI) LPD explained in detail along extraction expression MI gain.