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 the light, also known as phototaxis. We used three methods to obtain the solutions, the generalized Kudryashov method, the <inl...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/10/2352 |
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| author | Alejandro León-Ramírez Oswaldo González-Gaxiola Guillermo Chacón-Acosta |
| author_facet | Alejandro León-Ramírez Oswaldo González-Gaxiola Guillermo Chacón-Acosta |
| author_sort | Alejandro León-Ramírez |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mrow><mo>−</mo><mi>R</mi><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow></msup></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-11T03:31:39Z |
| format | Article |
| id | doaj.art-c5f822a3e9c7470687719c919c27d6f4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:31:39Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c5f822a3e9c7470687719c919c27d6f42023-11-18T02:19:44ZengMDPI AGMathematics2227-73902023-05-011110235210.3390/math11102352Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration SchemesAlejandro León-Ramírez0Oswaldo González-Gaxiola1Guillermo Chacón-Acosta2Postgraduate Studies in Natural Sciences and Engineering, Universidad Autónoma Metropolitana-Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, MexicoApplied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, MexicoApplied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, MexicoIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mrow><mo>−</mo><mi>R</mi><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow></msup></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/11/10/2352diffusion equationstraveling wavesphototaxisbacterial motionbiological aggregation |
| spellingShingle | Alejandro León-Ramírez Oswaldo González-Gaxiola Guillermo Chacón-Acosta Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes Mathematics diffusion equations traveling waves phototaxis bacterial motion biological aggregation |
| title | Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes |
| title_full | Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes |
| title_fullStr | Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes |
| title_full_unstemmed | Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes |
| title_short | Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes |
| title_sort | analytical solutions to the chavy waddy kolokolnikov model of bacterial aggregates in phototaxis by three integration schemes |
| topic | diffusion equations traveling waves phototaxis bacterial motion biological aggregation |
| url | https://www.mdpi.com/2227-7390/11/10/2352 |
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