(3+1)维Hirota双线性方程的lump解  

Lump Solutions of(3+1)-dimensional Hirota Bilinear Equation

作　　者：秦春艳 晋守博[1] 任敏 李壮壮[1] QIN Chun-yan;JIN Shou-bo;REN Min;LI Zhuang-zhuang(School of Mathematics and Statistics,Suzhou University,Suzhou 234000,Anhui,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《兰州文理学院学报（自然科学版）》2024年第5期1-7,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：安徽省高校自然科学研究项目(KJ2021A1102,2022AH040207,KJ2021A1002,2022AH051370)。

摘　　要：非线性发展方程是现代数学的一重要分支,其精确解的计算一直都是非线性科学领域的主流与焦点问题.lump解是精确解析解的一种特殊形式,以(3+1)维Hirota双线性方程为例对此展开研究.首先,利用Hirota双线性方法研究其经典lump解.其次,以双线性神经网络方法为基础,借助符号计算方法,得到方程的高阶lump解,主要是4阶lump解的计算.最后,通过对参数赋予一些特殊值,借助Maple软件,绘制出相关的三维图、密度图、相图以及传播图等,得到一些新的现象,同时展示了所求出的解的动力学行为.Nonlinear evolution equations are an important branch of modern mathematics,and the calculation of their exact solutions has always been the mainstream and focus of nonlinear science.Lump solutions are a special form of exact analytic solutions.This paper takes(3+1)-dimensional Hirota bilinear equation as an example to study this.Firstly,the classical lump solution is studied by using Hirota bilinear method.Then,based on bilinear neural network method,with the help of symbolic calculation method,the higher order lump solution of the equation is obtained,mainly the calculation of fourth-order lump solution.By assigning some special values to the parameters,with the help of Maple software,the related three-dimensional plots,density plots,phase plots and propagation plots are drawn,and some new phenomena are obtained.At the same time,the dynamic behavior of the solution is shown.

关 键 词：(3+1)维Hirota双线性方程 符号计算法 双线性神经网络方法 lump解 

分 类 号：O175.29[理学—数学]