Soliton dynamics and chaotic analysis of the Biswas–Arshed model

In this study, we investigate the Biswas–Arshed (BA) model, applicable in various fields such as fluid mechanics, laser science, and nonlinear optics. We employ the direct algebraic procedure, the modified rational sine–cosine process, and the 1G^′ approach to obtain soliton dynamics of the mentioned model. Chaotic behavior and sensitivity analysis of the BA model are also investigated using a planar dynamic system. As a result, periodic, quasi-periodic, and chaotic patterns are obtained from the suggested nonlinear model. We also obtain various soliton solutions from this model with novel properties. From the proposed equation, we can obtain periodic waves with bright solitons, bright-dark solitons, dark solitons, breather waves with singularities, double periodic waves, periodic waves with singularities, bright solitons with singularities, multiple bright dark breather waves with singularities, and multiple bright breather waves with singularities. Certain features of the outcomes are exhibited in 2D, 3D, and density views. The work presented is innovative as it offers valuable insights into the governing model's intricate behaviors and diverse waveforms through extensive analysis. This study also contributes to understanding real-world problems by incorporating waveform properties, bifurcation analysis, chaotic dynamics, and sensitivity tests.