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...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.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.12375006the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。
文摘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.
