Retrieval of diverse soliton, lump solutions to a dynamical system of the nonlinear Biswas–Milovic equation and stability analysis

In nature, complex phenomena can be described by the system of nonlinear partial differential equations. The solitons are significant nonlinear phenomenon in optics that appears when the nonlinearity precisely balances the dispersion. The key objective of this research is to investigate a range of optical soliton solutions for the nonlinear Biswas–Milovic (NLBM) equation in a magneto-optical wave guiding coupling system with Kudryashov’s law of refractive index using two modified analytical approaches. We employed the unified technique and the Hirota bilinear method to extract fresh solitary wave solutions with three separate interaction phenomena, including the multi-wave, double exponential, and homoclinic breather phenomena. These exact solutions are successfully given by diverse complicated wave-structures of solutions such as multipeak solitons, multipeak solitons with multiple kink waves, breather, dark, single, and periodic soliton solutions. These solutions are applicable in plasma physics, optical fibers, fluid dynamics, and other domains. We also investigate the sensitivity analysis of the governing model. Furthermore, we explain our chosen model’s stability analysis, which ensures that the governing model is stable. Many selected solutions are also visually shown to signify the physical nature of the derived solutions. The obtained soliton solutions confirm the authenticity and efficacy of the proposed procedures.