The step-wise construction of solitary solutions to Riccati equations with diffusive coupling

Romas Marcinkevicius; Inga Telksniene; Tadas Telksnys; Zenonas Navickas; Minvydas Ragulskis; Romas Marcinkevicius; Inga Telksniene; Tadas Telksnys; Zenonas Navickas; Minvydas Ragulskis

doi:10.3934/math.20231568

AIMS Mathematics

2023, Volume 8, Issue 12: 30683-30703. doi: 10.3934/math.20231568

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Research article

The step-wise construction of solitary solutions to Riccati equations with diffusive coupling

1.
Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania
2.
Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

Received: 23 June 2023 Revised: 31 October 2023 Accepted: 03 November 2023 Published: 13 November 2023
MSC : 35C08, 34A25, 68W30

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.
- operator calculus,
- solitary solution,
- Riccati equation,
- computer algebra
Citation: Romas Marcinkevicius, Inga Telksniene, Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis. The step-wise construction of solitary solutions to Riccati equations with diffusive coupling[J]. AIMS Mathematics, 2023, 8(12): 30683-30703. doi: 10.3934/math.20231568

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Abstract

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.

References

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