AccScience Publishing / IJOCTA / Volume 16 / Issue 2 / DOI: 10.36922/IJOCTA025510233
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RESEARCH ARTICLE

Various solutions of (2+1)-dimensional sixth-order breaking soliton systems using bilinear neural network method

Nguyen Minh Tuan1† ,  Nguyen Hong Son1† ,  Huynh Trong Thua1*
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1 Department of Computer Science, Faculty of Information Technology, Posts and Telecommunications Institute of Technology City, 11 Nguyen Dinh Chieu, Sai Gon ward, Ho Chi Minh city, Viet Nam
†These authors contributed equally to this work.
IJOCTA 2026, 16(2), 717–731; https://doi.org/10.36922/IJOCTA025510233
Received: 17 December 2025 | Revised: 24 January 2026 | Accepted: 10 February 2026 | Published online: 30 March 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper firstly introduces the (2+1)-dimensional sixth-order breaking soliton system (SBSS) using the bilinear neural network method, providing many types of solutions. A new structure of the SBSS is investigated, and new solutions are gathered. The solutions are expressed in terms of basic activation functions and are derived by applying these activation functions. Using the Hirota bilinear operator, the original nonlinear partial differential equation is reduced to a more tractable form. The bilinear neural network approach yields various classes of solutions, including kink, rogue, peak, breather, lump-type, and spike-type solutions. These solutions are expressed in terms of elementary functions, revealing the various dynamical behaviors inherent in the system. The results obtained not only generalize known solutions but also illustrate a deeper insight into the complex wave propagation phenomena described by the sixth-order breaking soliton equation.

Keywords
Breaking soliton system
Bilinear neural network method (BNNM)
Softmax method
High-order soliton equations
Solitary wave solutions
Analytic exact solution
Funding
Posts and Telecommunications Institute of Technology in Ho Chi Minh City, Vietnam Number 999/QD-HV.
Conflict of interest
The authors declare no conflict of interest.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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