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

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.