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

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dc.contributor.authorKudryashov, N.A.
dc.contributor.authorLavrova, S. F.
dc.contributor.authorКудряшов, Николай Алексеевич
dc.contributor.authorЛаврова, София Федоровна
dc.date.accessioned2024-12-27T09:43:16Z
dc.date.available2024-12-27T09:43:16Z
dc.date.issued2023
dc.description.abstractThe Chavy-Waddy-Kolokolnikov model for the description of bacterial colonies is considered. In order to establish if the mathematical model is integrable, the Painleve test is conducted for the nonlinear ordinary differential equation which corresponds to the fourth-order partial differential equation. The restrictions on the mathematical model parameters for ordinary differential equations to pass the Painleve test are obtained. It is determined that the method of the inverse scattering transform does not solve the Cauchy problem for the original mathematical model, since the corresponding nonlinear ordinary differential equation passes the Painleve test only when its solution is stationary. In the case of the stationary solution, the first integral of the equation is obtained, which makes it possible to represent the general solution in the quadrature form. The stability of the stationary points of the investigated mathematical model is carried out and their classification is proposed. Periodic and solitary stationary solutions of the Chavy-Waddy-Kolokolnikov model are constructed for various parameter values. To build analytical solutions, the method of the simplest equations is also used. The solutions, obtained in the form of a truncated expansion in powers of the logistic function, are represented as a closed formula using the formula for the Newton binomial.
dc.identifier.citationKudryashov, N.A. Painleve Test, Phase Plane Analysis and Analytical Solutions of the Chavy-Waddy-Kolokolnikov Model for the Description of Bacterial Colonies / Kudryashov, N.A., Lavrova, S.F. // Mathematics. - 2023. - 11. - № 14. - 10.3390/math11143203
dc.identifier.doi10.3390/math11143203
dc.identifier.urihttps://www.doi.org/10.3390/math11143203
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85174717771&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:001036673900001
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/29243
dc.relation.ispartofMathematics
dc.titlePainleve Test, Phase Plane Analysis and Analytical Solutions of the Chavy-Waddy-Kolokolnikov Model for the Description of Bacterial Colonies
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue14
oaire.citation.volume11
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