Properties of the generalized Chavy-Waddy-Kolokolnikov model for of bacterial colonies

The Chavy-Waddy-Kolokolnikov model with dispersion for describing bacterial colonies is considered. This mathematical model is described by a nonlinear partial differential equation of the fourth order. This equation does not pass the Painleve test and the Cauchy problem cannot be solved by the inverse scattering transform. Some new properties of the Chavy-Waddy- Kolokolnikov model are studied. Analytical solutions of the equation in traveling wave variables are found taking into account the dispersion coefficient. It is shown that, unlike the model without dispersion, a bacterial cluster can move, which allows us to consider dispersion as some kind of control for bacterial colony. Using numerical modeling, we also demonstrate that the initial concentration of bacteria in the form of a random distribution over time transforms into a periodic wave, followed by a transition to a stationary solitary wave without taking dispersion into account.

Automated summary

The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.