1. Properties of the generalized Chavy-Waddy–Kolokolnikov model for description of bacterial colonies.
- Author
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Kudryashov, Nikolay A, Kutukov, Aleksandr A, and Lavrova, Sofia F
- Subjects
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BACTERIAL colonies , *INVERSE scattering transform , *NONLINEAR differential equations , *PARTIAL differential equations , *DISTRIBUTION (Probability theory) , *ANT algorithms - Abstract
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 Painlevé 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. • The Chavy-Waddy–Kolokolnikov model with dispersion is considered. • Analytical solutions of model are found taking traveling wave reduction. • Results of numerical modeling for bacterial colonies are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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