Exploring the Chavy–Waddy–Kolokolnikov Model: Analytical Study via Recently Developed Techniques

This work explores the analytical soliton solutions to the Chavy–Waddy–Kolokolnikov equation (CWKE), which is a well-known equation in biology that shows how light-attracted bacteria move together. This equation is very useful for analyzing pattern creation, instability regimes, and minor changes in linear situations since bacterial movement is very sensitive to outside factors such as light and heat. The three recently developed analytical methods, such as the modified Riccati equation mapping approach, the modified extended tanh-expansion method, and the modified generalized exponential rational function method, are applied to find the desired solutions. The CWKE is converted into a nonlinear ordinary differential equation by using these methods combined with several transformations, such as the M-fractional transformation. This lets us to find different solutions, such as dark, single, bright–dark, bright, and mixed solitons. Moreover, the graphical representations of the solutions are presented for a better understanding of how fractional parameters affect wave dynamics. The suggested methods show that they can make accurate and dependable traveling wave solutions for a wide range of nonlinear evolution equations. The results of this study should help us understand how bacteria adapt, especially when it comes to chemotaxis and phototaxis.