约化的(3+1)维Hirota方程的呼吸波解、lump解和半有理解  

Breather Wave Solutions,Lump Solutions and Semi-Rational Solutions of a Reduced(3+1)Dimensional Hirota Equation

作　　者：房春梅 田守富 Fang Chunmei;Tian Shoufu(Department of Mathematics and Statistics,Jining Normal University,Inner Mongolia Ulanqab 012000;Department of Mathematics,China University of Mining and Technology,Jiangsu Xuzhou 221116)

机构地区：[1]集宁师范学院数学与统计学院,内蒙古乌兰察布012000 [2]中国矿业大学数学学院,江苏徐州221116

出　　处：《数学物理学报（A辑）》2022年第3期775-783,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11975306);内蒙古自治区高等学校科学研究项目(NJZY20248,NJZY22307)~。

摘　　要：该文利用长波极限方法研究了(3+1)维Hirota方程在维数约化z=x下的精确解.首先利用贝尔多项式构造了其双线性形式.基于双线性形式,对N-孤子解做某些参数约束,获得了n-阶呼吸波解.其次,利用长波极限方法获得了高阶lump波解.最后导出了一阶,二阶lump波解分别与单孤子解的混合解,即半有理解.所有得到的解都通过Maple软件进行物理特征分析.In this paper,the long wave limit method is used to study the exact solutions of the(3+1)dimensional Hirota equation under dimensional reduction z=x.First,the bilinear form is constructed by using Bell polynomials.Based on the bilinear form,the n-order breather wave solutions are obtained under some parameter constraints on the N-order soliton solution.Secondly,by using the long wave limit method,high order lump wave solutions are obtained.Finally,the combined solutions of the first-order,second-order lump wave solutions and single solitary wave solutions are derived,i.e.semi-rational solutions.All the obtained solutions were analyzed with Maple software for physical characteristics.

关 键 词：(3+1)维Hirota方程 双线性形式 呼吸波解 Lump波解 半有理解 

分 类 号：O175.24[理学—数学]