Optimising the bifurcation analysis, phase portrait, chaotic behaviour, and optical soliton solutions of the Biswas–Milovic model in fibre optic communication

This work presents an exclusive study on the (1 + 1)-dimensional Biswas-Milovic model with power-law nonlinearity, focusing on bifurcation analysis, phase portrait, and dynamic behaviour of optical wave propagation. This model is a momentous nonlinear evolution equation to describe optical pulses in optical fibre communication and nonlinear wave dynamics. The bifurcation analysis provides insights into the qualitative behaviour of the system, revealing critical parameter thresholds at which solution structure changes. We also examine the chaotic nature of the system using a trigonometric perturbation term. The unpredictable and extremely sensitive behaviour displayed by certain dynamic systems is referred to as chaos. By employing the modified simple equation technique to solve nonlinear equations, we derive exact soliton solutions that describe the propagation of optical pulses in nonlinear media. The derived solutions include cross-periodic soliton, Bright and dark periodic waves, bright bell soliton, bright-dark bell soliton, and periodic breather wave solutions, highlighting the model's versatility in describing diverse wave phenomena. These findings extend the analytical understanding of the Biswas-Milovic model and contribute to the development of advanced techniques for studying nonlinear optical systems. The results are expected to have applications in fibre optics, optical signal processing, and other areas involving nonlinear wave propagation.