A new (3 + 1) dimensional Hirota bilinear equation: Periodic, rogue, bright and dark wave solutions by bilinear neural network method

Abstract

This study deals with a new (3 + 1) dimensional Hirota equation that emerges in shallow water waves theory. Considering the bilinear form of this equation, the bilinear neural network method was applied. At this point, new activation functions have been proposed by using both single-layer and multi-layer neurons such as 4-2-2 and 4-2-3 types. As a result, a periodic type I–II, rogue, bright, and dark wave solutions with physical properties have been systematically produced via Maple symbolic software. In order to better consider the characteristics and dynamic structure of these revealed solution forms, 3D, contour, density, and 2D dimensional graphics are drawn for the appropriate values of the parameters. Bilinear neural network method includes many existing classical test functions and is an effective, robust and systematic approach.