Various solutions of the (2+1)-dimensional Hirota–Satsuma–Ito equation using the bilinear neural network method

• Published in: Chinese journal of physics (Taipei) 2023-06, Vol.83, p.292-305
• Main Authors: Zhu, Guangzheng, Wang, Hailing, Mou, Zhen-ao, Lin, Yezhi
• Format: Article
• Language: English
• Subjects: Bilinear neural network method; D-operator; Hirota bilinear form; Hirota–Satsuma–Ito equation
• ISSN: 0577-9073
• DOI: 10.1016/j.cjph.2023.03.016

The Hirota–Satsuma–Ito equation is a well-known nonlinear partial differential equation in fluid mechanics. This paper deals with a (2+1)-dimensional Hirota–Satsuma–Ito equation through the bilinear neural network method. In the bilinear neural network method, a variety of neural network structures, including the single hidden layer and multi hidden layers neural network, are used to obtain the analytical solutions which are summarized to be of the following types: breathers, interaction of opposite waves, interaction of rogue wave and soliton, traveling waves and rogue waves. The feasibility and advantage of the proposed structures are illustrated by seeking these new solutions. Wave characteristics are exhibited by some plots of these obtained solutions. •We use the bilinear neural network method to find solutions of HSI equation.•New activation functions were used to find more abundant solutions.•Comparing with some ordinary methods, this method can obtain accurate analytical solutions.•Our paper reflects some of the new nonlinear characteristics of the HSI equation.