Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies

The Chavy–Waddy–Kolokolnikov model for the description of bacterial colonies is considered. In order to establish if mathematical integrable, Painlevé test conducted nonlinear ordinary differential equation which corresponds fourth-order partial equation. restrictions on parameters equations pass are obtained. It determined that method inverse scattering transform does not solve Cauchy problem original model, since corresponding passes only when its solution stationary. case stationary solution, first integral obtained, makes it possible represent general in quadrature form. stability points investigated carried out and their classification proposed. Periodic solitary solutions constructed various parameter values. To build analytical solutions, simplest also used. obtained form a truncated expansion powers logistic function, represented as closed formula using Newton binomial.