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

作　　者：Zhao Zhao Bo Ren 

机构地区：[1]Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou 310014,China

出　　处：《Communications in Theoretical Physics》2025年第3期1-11,共11页理论物理通讯(英文版)

基　　金：supported by the National Natural Science Foundation of China under Grant No.12375006;the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。

摘　　要：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.

关 键 词：bilinear transformation BNNM double-layer model exact analytical solution 

分 类 号：O17[理学—数学]