中北大学学报（自然科学版）2018，Vol.39Issue(1)：25-31,7.DOI:10.3969/j.issn.1673-3193.2018.01.005
一个(3+1)维非线性演化方程的周期波解
The Periodic Wave Solutions of a (3+1 )Dimensional Nonlinear Evolution Equation
摘要
Abstract
On the basis of a general multidimensional Riemann theta function,a direct generalization of the bilinear method was established to construct Riemann theta functions periodic wave solutions for (3+1)dimensional nonlinear evolution equation.Among the multi periodic wave solutions,the one pe-riodic waves'surface pattern is one dimensional.In two independent horizontal directions,the two peri-odic waves have two independent periods,so they are a straight-forward generalization of one periodic waves and their surface pattern is two dimensional.Based on the bilinear representation of the nonlinear equation,one soliton solutions and two soliton solutions of the (3+1 )dimensional nonlinear partial dif-ferential equation were constructed using the bilinear method.The relations between the two kinds of solutions are described by a limiting procedure and the asymptotic behavior of the quasiperiodic wave so-lutions are analyzed accordingly.It is presented the periodic wave solutions tend to soliton solutions un-der a small amplitude limit.关键词
(3+1)维非线性演化方程/周期波解/孤子解/渐近性态/黎曼theta函数Key words
(3+1)dimensional nonlinear evolution equation/periodic wave solutions/soliton solutions/asymptotic behavior/Riemann theta function分类
数理科学引用本文复制引用
郭婷婷..一个(3+1)维非线性演化方程的周期波解[J].中北大学学报（自然科学版）,2018,39(1):25-31,7.基金项目
山西大学商务学院科研基金资助项目(2016028) （2016028）
