Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes

Abstract

In this work, we find analytical solutions to the Chavy-Waddy–Kolokolnikov equation, a continuum approximation for modeling aggregate formation in bacteria moving toward the light, also known as phototaxis. We used three methods to obtain the solutions, the generalized Kudryashov method, the e−R(ξ)-expansion, and exponential function methods, all of them being very efficient for finding traveling wave-like solutions. Findings can be classified into the case where the nonlinear term can be considered a small perturbation of the linear case and the regime of instability and pattern formation. Standing waves and traveling fronts were also found among the physically interesting cases, in addition to recovering stationary spike-like solutions.