用Hirota双线性方法构造的高维sine-Gordon方程的新型精确解  

New Exact Solutions of Higher Dimensional sine-Gordon Equation Constructed by Hirota Bilinear Method

作　　者：黎倍祯 毛辉 LI Bei-zhen;MAO Hui(School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530100

出　　处：《南宁师范大学学报（自然科学版）》2023年第4期30-35,共6页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(12261061);广西自然科学基金项目(2022GXNSFAA 035598)。

摘　　要：该文运用Hirota双线性方法,通过反正切函数变换导出了二维sine-Gordon方程的双线性形式,然后对待定函数进行假设并选取适当的参数,构造了方程的新型精确解.还证明了一般的n维sine-Gordon方程也具有此类型的精确解.In this paper we derive the Hirota bilinear form of the two-dimensional sine-Gordon equation by the transformation of arc tangent function,then construct a new exact solution of the equation by making assumptions about the undetermined functions and selecting appropriate parameters.We show that the general n-dimensional sine-Gordon equation also has an exact solution of this type.

关 键 词：HIROTA双线性方法 函数变换 高维sine-Gordon方程 精确解 

分 类 号：O175.2[理学—数学]