约化的(3+1)维Hirota方程的呼吸波解、lump解和半有理解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 775-783.

约化的(3+1)维Hirota方程的呼吸波解、lump解和半有理解

房春梅^1,*(),田守富²()

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

收稿日期:2021-07-22 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 房春梅 E-mail:dllgfcmmxl@163.com;shoufu2006@126.com
作者简介:田守富, E-mail: shoufu2006@126.com
基金资助:
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);内蒙古自治区高等学校科学研究项目(NJZY22307)

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

Chunmei Fang^1,*(),Shoufu Tian²()

¹ Department of Mathematics and Statistics, Jining Normal University, Inner Mongolia Ulanqab 012000
² Department of Mathematics, China University of Mining and Technology, Jiangsu Xuzhou 221116

Received:2021-07-22 Online:2022-06-26 Published:2022-05-09
Contact: Chunmei Fang E-mail:dllgfcmmxl@163.com;shoufu2006@126.com
Supported by:
the NSFC(11975306);the Higher Educational Scientific Research Projects of Inner Mongolia Autonomous Region(NJZY20248);the Higher Educational Scientific Research Projects of Inner Mongolia Autonomous Region(NJZY22307)

摘要/Abstract

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.

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

Abstract:

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.

Key words: The (3+1)dimensional Hirota equation, Bilinear representation, Breather solutions, Lump wave solutions, Semi-rational solutions

中图分类号:

O175.24

房春梅,田守富. 约化的(3+1)维Hirota方程的呼吸波解、lump解和半有理解[J]. 数学物理学报, 2022, 42(3): 775-783.

Chunmei Fang,Shoufu Tian. Breather Wave Solutions, Lump Solutions and Semi-Rational Solutions of a Reduced (3+1)Dimensional Hirota Equation[J]. Acta mathematica scientia,Series A, 2022, 42(3): 775-783.

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