Periodic solutions, breather, lump and interaction solutions of a generalized (2+1)-dimensional Hirota bilinear equation via the bilinear neural network method

Abstract The main focus of this paper is to address a generalized (2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method. The paper presents the periodic solutions through a single-layer model of [3-4-1], followed by breather, lump and their interaction solutions by using double-layer models of [3-3-2-1] and [3-3-3-1], respectively. A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel [3-(2+2)-4-1] model, where a specific hidden layer is partitioned into two segments for subsequent operations. Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.