Perturbed Biswas–Milovic equation with Kudryashov’s law of refractive index: analysis and solutions for nonlinear optical systems

This study examines the perturbed Biswas–Milovic equation (PBME) with Kudryashov’s law of refractive index. For accomplishing this goal, the \(\Psi ^{6}\) ${\mathrm{\Psi }}^6$ -model expansion methodology was created. Jacobi-elliptic, bright, singular, dark and singular periodic solutions are found in this study.To improve optical technology, the PBME helps comprehend nonlinear effects, optimize device performance, characterize materials, create advanced optical systems, and improve biomedical imaging. Jacobi-elliptic solution, bright, dark, and periodic solution are all represented in 3D and 2D dimensional representations.