一个高维非线性方程的黎曼theta函数周期波解  

Periodic Wave Solutions of Riemann Theta Function for a High Dimensional Nonlinear Function

作　　者：郭婷婷[1] GUO Ting-ting(College of Business,Shanxi University,Taiyuan 030031,China)

机构地区：[1]山西大学商务学院,山西太原030031

出　　处：《中北大学学报（自然科学版）》2019年第1期13-17,共5页Journal of North University of China(Natural Science Edition)

摘　　要：基于非线性偏微分方程的Hirota双线性表示,结合一般黎曼theta函数的周期性理论,得到构造(3+1)维非线性偏微分方程双周期波解的方法,这种双周期波解是黎曼theta函数系列的解.该解有一个相位变量,因而是一维的.函数的相位变量有两个基本周期,因而这种解是双周期波解.经典的单孤子解与双周期波解之间的关系可以用一个极限过程来表示,当限制波的振幅很小时,该(3+1)维非线性偏微分方程的双周期波解会趋于其单孤波解.Based on Hirota bilinear representation of nonlinear partial differential equation and the periodic theory of general Riemann theta function,a method of constructing double periodic wave solutions for a(3+1)-dimensional nonlinear partial differential equation is established.The obtained double periodic wave solutions are theta function serial solutions.There is a single phase variable in the solution,so it is one-dimensional.There are two fundamental periods in the phase variable of the function,so the kind of solutions is double periodic wave solution.The relations between the classical one soliton solutions and the double periodic wave solutions are showed by a extreme procedure,it is obtained that the double periodic wave solutions of the(3+1)-dimensional nonlinear partial differential equation tends to the one soliton wave solution by making a small amplitude limit of the wave.

关 键 词：黎曼theta函数 (3+1)维非线性偏微分方程 单孤子解 双线性表示 双周期波解 

分 类 号：O129.35[理学—数学]