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

Alejandro León-Ramírez, Oswaldo González-Gaxiola () and Guillermo Chacón-Acosta
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Alejandro León-Ramírez: Postgraduate Studies in Natural Sciences and Engineering, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, Mexico
Oswaldo González-Gaxiola: Applied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, Mexico
Guillermo Chacón-Acosta: Applied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, Mexico

Mathematics, 2023, vol. 11, issue 10, 1-24

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.

Keywords: diffusion equations; traveling waves; phototaxis; bacterial motion; biological aggregation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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