| Title |
Constructing solitary solutions to nonlinear differential equations using AI-assisted differentiation operators / |
| Authors |
Telksnys, Tadas ; Telksnienė, Inga ; Marcinkevičius, Romas ; Navickas, Zenonas ; Ragulskis, Minvydas |
| DOI |
10.15388/DAMSS.15.2024 |
| eISBN |
9786090711125 |
| Full Text |
|
| Is Part of |
DAMSS: 15th conference on data analysis methods for software systems, Druskininkai, Lithuania, November 28-30, 2024.. Vilnius : Vilniaus universiteto leidykla, 2024. p. 113-114.. eISBN 9786090711125 |
| Abstract [eng] |
Constructing solitary solutions to nonlinear differential equations using AI-assisted differentiation operators By applying inverse balancing techniques in combination with an AI-assisted generalized differential operator method, we have derived deformed kink solitary solutions for a non-autonomous Riccati system that incorporates diffusive coupling. Such systems can be found in many applications, including biological applications, population dynamics modelling, and other areas. The solutions obtained do generalize kink solitary solutions within the classical solitary solution framework: while classical solitary solutions employ an exponential time transformation, deformed solitary solutions can utilize any non-singular transformation function. This allows for a much wider spectrum of solutions, which is not limited to the more traditional soliton framework but a rich variety of analytical forms. Furthermore, the class of differential equations that can be considered using these techniques is also significantly widened due to the introduction of a nonautonomous term that may be present in both the original and image equations. However, the construction of these more general solutions is far from trivial, both analytically and computationally. It requires a multi-stage process that involves analytically solving a specific system of nonlinear equations related to both differential equations and solution parameters. While obtaining a single solution for the aforementioned system is fairly straightforward, listing all possible cases is a process that is not feasible to perform by hand, necessitating the use of more advanced techniques. Standard tools are difficult to apply since there are not many techniques that work smoothly with symbolic rather than numerical data. For that reason, a custom AI-based tool is employed to analyze the symbolic big data set, enabling the elimination of numerous degenerate cases and significantly enhancing the efficiency of the proposed approach. This tool assists with the pruning of so-called deadend branches, which do not result in constant or degenerate solutions. |
| Published |
Vilnius : Vilniaus universiteto leidykla, 2024 |
| Type |
Conference paper |
| Language |
English |
| Publication date |
2024 |
| CC license |
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