The step-wise construction of solitary solutions to Riccati equations with diffusive coupling
A novel scheme based on the generalized differential operator and computer algebra was used to construct solitary solutions to a system of Riccati differential equations with diffusive coupling. The presented approach yields necessary and sufficient existence conditions of solitary solutions with re...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231568?viewType=HTML |
| _version_ | 1797450915745103872 |
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| author | Romas Marcinkevicius Inga Telksniene Tadas Telksnys Zenonas Navickas Minvydas Ragulskis |
| author_facet | Romas Marcinkevicius Inga Telksniene Tadas Telksnys Zenonas Navickas Minvydas Ragulskis |
| author_sort | Romas Marcinkevicius |
| collection | DOAJ |
| description | A novel scheme based on the generalized differential operator and computer algebra was used to construct solitary solutions to a system of Riccati differential equations with diffusive coupling. The presented approach yields necessary and sufficient existence conditions of solitary solutions with respect to the system parameters. The proposed stepwise approach enabled the derivation of the explicit analytic solution, which could not be derived using direct balancing techniques due to the complexity of algebraic relationships. Computational experiments were used to demonstrate the efficacy of proposed scheme. |
| first_indexed | 2024-03-09T14:47:24Z |
| format | Article |
| id | doaj.art-654277a5cf5641fcb74e02a2c513580e |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-09T14:47:24Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-654277a5cf5641fcb74e02a2c513580e2023-11-27T01:37:12ZengAIMS PressAIMS Mathematics2473-69882023-11-01812306833070310.3934/math.20231568The step-wise construction of solitary solutions to Riccati equations with diffusive couplingRomas Marcinkevicius0Inga Telksniene1Tadas Telksnys2 Zenonas Navickas3Minvydas Ragulskis41. Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania2. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania2. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania2. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania2. Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, LithuaniaA novel scheme based on the generalized differential operator and computer algebra was used to construct solitary solutions to a system of Riccati differential equations with diffusive coupling. The presented approach yields necessary and sufficient existence conditions of solitary solutions with respect to the system parameters. The proposed stepwise approach enabled the derivation of the explicit analytic solution, which could not be derived using direct balancing techniques due to the complexity of algebraic relationships. Computational experiments were used to demonstrate the efficacy of proposed scheme.https://www.aimspress.com/article/doi/10.3934/math.20231568?viewType=HTMLoperator calculussolitary solutionriccati equationcomputer algebra |
| spellingShingle | Romas Marcinkevicius Inga Telksniene Tadas Telksnys Zenonas Navickas Minvydas Ragulskis The step-wise construction of solitary solutions to Riccati equations with diffusive coupling AIMS Mathematics operator calculus solitary solution riccati equation computer algebra |
| title | The step-wise construction of solitary solutions to Riccati equations with diffusive coupling |
| title_full | The step-wise construction of solitary solutions to Riccati equations with diffusive coupling |
| title_fullStr | The step-wise construction of solitary solutions to Riccati equations with diffusive coupling |
| title_full_unstemmed | The step-wise construction of solitary solutions to Riccati equations with diffusive coupling |
| title_short | The step-wise construction of solitary solutions to Riccati equations with diffusive coupling |
| title_sort | step wise construction of solitary solutions to riccati equations with diffusive coupling |
| topic | operator calculus solitary solution riccati equation computer algebra |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231568?viewType=HTML |
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