One of the important problems arising in biology science is the bacteria motion that surrenders to some operators as
light, heat…,etc. The Chavy-Waddy-Kolokolnikov equation (CWKE) is considered one of the famous models in biology branch
that is very valuable in the modeling bacteria collective formation attracted to the light. Hereby, we will study this effective model
to construct the soliton behaviors of this model. Hereby, we will choose two of the impressive semi-analytical methods, namely,
the extended simple equation method (ESEM) and the (G’/G)-expansion method to extract the analytical solutions of this model
and derive the soliton behaviors through the 2-kind and 3-kind graphs of these obtained solutions. The two suggested methods are
two famous of the ansatz methods that surrender to the homogenous balance rule, used to construct the exact solution for nonlinear
partial differential equation and examined before for many other nonlinear evolution equations and usually realize good results.
In addition, we will derive the numerical solutions identical for achieved analytical solutions by using the differential transform
method (DTM) which is one of the most, efficient numerical methods. To show the newly of our results, we will make comparison
for the obtained soliton solutions behaviors with that previously realized by other authors.