Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 775-783.

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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;
  • 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)


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

CLC Number: 

  • O175.24