• 论文 •

### 约化的(3+1)维Hirota方程的呼吸波解、lump解和半有理解

1. 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 Fang1,*(),Shoufu Tian2()

1. 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)

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.

• O175.24