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

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