The auxiliary equation method for the construction of deformed solitary solutions to the model of tumor-immune system interaction

R. Marcinkevičius; R. Mickevičius; Z. Navickas; I. Telksnienė; T. Telksnys; M. Ragulskis; R. Marcinkevičius; R. Mickevičius; Z. Navickas; I. Telksnienė; T. Telksnys; M. Ragulskis

doi:10.3934/math.20251139

AIMS Mathematics

2025, Volume 10, Issue 11: 25729-25755. doi: 10.3934/math.20251139

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The auxiliary equation method for the construction of deformed solitary solutions to the model of tumor-immune system interaction

1.
Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania
2.
Urology Clinic, Lithuanian University of Health Sciences, Eiveniu 2, Kaunas LT-50009, Lithuania
3.
Department of Mathematical Modelling, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

Received: 28 August 2025 Revised: 19 October 2025 Accepted: 29 October 2025 Published: 10 November 2025
MSC : 35C08, 34A25, 68W30

The auxiliary equation method for the construction of deformed solitary solutions to the mathematical model of tumor-immune system interaction is presented in this paper. The investigated model does not admit classical solitary solutions. Special techniques based on symbolic computations are used to construct deformed solitary solutions by simultaneously avoiding the inherent additional constraints to the model parameters. It is demonstrated that the introduction of the auxiliary equation does not drop any solutions from the original system. Also, deformed solitary solutions do not depend on the parameters of the auxiliary equations. Analytical and computations experiments are used to demonstrate the efficacy of the proposed method.
- soliton,
- auxiliary equation,
- uncontrolled dynamics,
- constraint
Citation: R. Marcinkevičius, R. Mickevičius, Z. Navickas, I. Telksnienė, T. Telksnys, M. Ragulskis. The auxiliary equation method for the construction of deformed solitary solutions to the model of tumor-immune system interaction[J]. AIMS Mathematics, 2025, 10(11): 25729-25755. doi: 10.3934/math.20251139

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Abstract

The auxiliary equation method for the construction of deformed solitary solutions to the mathematical model of tumor-immune system interaction is presented in this paper. The investigated model does not admit classical solitary solutions. Special techniques based on symbolic computations are used to construct deformed solitary solutions by simultaneously avoiding the inherent additional constraints to the model parameters. It is demonstrated that the introduction of the auxiliary equation does not drop any solutions from the original system. Also, deformed solitary solutions do not depend on the parameters of the auxiliary equations. Analytical and computations experiments are used to demonstrate the efficacy of the proposed method.

References

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