Optical soliton solutions for the Chavy-Waddy-Kolokolnikov model for bacterial colonies using two improved methods

In this paper, we use direct algebra and improved generalized Riccati equation methods to investigate optical soliton solutions to the Chavy-Waddy-Kolokolnikov model for bacterial colonies. The model is effective at phototaxis, which is the generation of bacterial aggregates that move toward the light. The model's solitary wave solutions are obtained using the direct algebra and Ricatti equation methods, which take into account the minor perturbations of the linear case as well as the regimes of pattern generation and instability. For each case, we determined the dynamic of optical soliton solutions for the model, which includes hyperbolic, periodic soliton solutions for the linear case and stationary spike-like solutions for the nonlinear case. The methods produced several types of hyperbolic, periodic, and exponential solutions for this model that were not previously specified in the literature. We also presented the 2D and 3D graphs to show the kink, bright, and dark solitary wave structures with suitable numerical values. The obtained solutions will be of great importance in chemotaxis and phototaxis bacterial adaptations.