非线性尘埃等离子体孤立子波变分迭代解  

The Variational Iteration Solution for Nonlinear Soliton in Dusty Plasma

作　　者：徐建中 汪维刚 莫嘉琪 XU Jian-zhong;WANG Wei-gang;MO Jia-qi(Department of Electronics and Information Engineering,Bozhou University,Bozhou 236800;Department of Basic,Hefei Preschool Education College,Hefei 230011;School of Mathematics&Statistics,Anhui Normal University,Wuhu 241003)

机构地区：[1]亳州学院电子与信息工程系,亳州236800 [2]合肥幼儿师范高等专科学校基础部,合肥230011 [3]安徽师范大学数学与统计学院,芜湖241003

出　　处：《工程数学学报》2020年第4期459-468,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(41275062);安徽省高校自然科学研究重点项目(KJ2018A0964,KJ2019A1261,KJ2019A1303);安徽省高校优秀青年人才支持计划项目(gxyq2018116).

摘　　要：在全球气候变暖的极端反常的情形下,大气尘埃的扩散现象会带来巨大的灾害.本文研究了大气尘埃等离子体扩散的一类广义非线性孤立子波模型.首先对非扰动情形下利用待定系数法得到孤立子波解的解析表示式.其次用广义变分迭代的方法求出对应的变分乘子并构造变分迭代式,依次求出孤子波的各次迭代解.然后用行波变换得到广义非线性尘埃等离子体扰动模型的孤立子波的各次近似解.最后,由得到解的近似函数序列据变分理论知,在自变量的一定区域内此序列为一致收敛的.因此便证明了迭代解的极限函数是尘埃等离子体低频振动非线性方程的精确解.本文得到的近似解是尘埃等离子体的低频振动孤立子波的近似解析解,据它可用解析运算来求出相关量的物理性态,如孤立子波的波峰值.可以根据本文理论采取相应措施,避免出现电荷超高密度的聚集而导致放电击穿现象等.Under the global climate warming condition,the dusty plasma diffusing phenomenon may bring a huge havoc.In this paper a class of generalized nonlinear solitary wave model of atmosphere dusty plasma diffusion was considered.Firstly,at typical non-disturbed situation,the analytic expression of solitary wave solution was obtained by using the undetermined coefficient method.Then from the method of generalized variation iteration,the variation multiplier was solved and the generalized variation iteration was constructed.Then we found out various iteration solutions of solitary waves.Further,the solitary wave of corresponding model for generalized nonlinear dusty plasma was obtained using a transform of travelling waves.Finally,from the homologous variation theory for the function sequence of obtained approximate solution,it is an uniformly convergent sequence on the corresponding argument area.Thus the limiting function from iteration solutions is the exact solution to the low frequency vibrated nonlinear equation for dusty plasma and the corresponding approximate solution is an approximate analytic solution.It can be further obtained dependent physical behaviors by using the analytic operation.For example,from the obtained peak value of the soliton wave,as corresponding measures,it avoid arises super-high density assemble physical behaviors of cause electric discharge spark-over phenomenon.

关 键 词：尘埃等离子体 变分迭代 近似解 

分 类 号：O175.29[理学—数学]