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Research Article | Open Access

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

R. Marcinkevičius1, R. Mickevičius2, Z. Navickas3, I. Telksnienė3, T. Telksnys3, M. Ragulskis3( )
Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania
Urology Clinic, Lithuanian University of Health Sciences, Eiveniu 2, Kaunas LT-50009, Lithuania
Department of Mathematical Modelling, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania
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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.

Keywords

solitonauxiliary equationuncontrolled dynamicsconstraint
CLC number: 35C08, 34A25, 68W30

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AIMS Mathematics
Volume 10 Issue 11,
November 2025
Pages 25729-25755
DOI: 10.3934/math.20251139

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Marcinkevičius R, Mickevičius R, Navickas Z, et al. The auxiliary equation method for the construction of deformed solitary solutions to the model of tumor-immune system interaction. AIMS Mathematics, 2025, 10(11): 25729-25755. https://doi.org/10.3934/math.20251139

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Received: 28 August 2025
Revised: 19 October 2025
Accepted: 29 October 2025
Published: 10 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)