Neural network-based symbolic calculation approach for solving the Korteweg–de Vries equation

Xiao-Ran Xie and Run-Fa Zhang

Chaos, Solitons & Fractals, 2025, vol. 194, issue C

Abstract: In this study, we propose an innovative method that combines neural network models and symbolic computing to quickly solve exact solutions to nonlinear partial differential equations (NLPDEs). By combining the high accuracy of symbolic computing with the strong adaptability of neural networks, this method significantly improves the efficiency and accuracy of decomputation. As an application, this paper uses the neural network symbol calculation method to successfully obtain multiple sets of new analytical solutions of the Korteweg–de Vries equation, and constructs a variety of new neural network models and their heuristic functions. This study provides a new computational paradigm for solving the exact solution of NLPDEs, and has the potential for a wide range of scientific and engineering applications.

Keywords: Symbolic computation; Exact solutions; KdV equation; Nonlinear partial differential equations (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925002450
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002450

DOI: 10.1016/j.chaos.2025.116232

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().