远场模型方程的同伦近似对称约化  

The approximate homotopy symmetry reduction for far-field model equation

作　　者：焦小玉[1,2] 

机构地区：[1]南京财经大学应用数学学院,南京210046 [2]上海交通大学物理系,上海200240

出　　处：《物理学报》2011年第12期1-7,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10735030;10905038;11071109)资助的课题~~

摘　　要：以同伦近似对称法为理论依据研究了远场模型方程,通过归纳各阶相似约化解和各阶相似约化方程的通式构造相应的同伦级数解.各阶相似约化方程均为线性变系数常微分方程,并且可以从零阶开始依次求解.同伦模型中的辅助参数影响同伦级数解的收敛性.The far-field model equation is investigated by the approximate homotopy symmetry method.Homotopy series solutions are constructed through summarizing the relevant general formulas for similarity reduction solutions and similarity reduction equations of differernt orders.Similarity reduction equations of different orders are linear variable coefficients ordinary differential equations,and can be solved one by one from zero-order similarity reduction equations.The auxiliary parameter in the homotopy model affects convergence of homotopy series solutions.

关 键 词：同伦近似对称法 远场模型方程 同伦级数解 

分 类 号：O241.82[理学—计算数学] O189.23[理学—数学]