利用Riccati方程求解Burgers方程再探  

Further Exploration of Solving Burgers Equation by Riccati Equation

作　　者：赵临龙 ZHAO Lin-long(School of Mathematics and Statistics,Ankang University,Ankang 725000,China)

机构地区：[1]安康学院数学与统计学院,陕西安康725000

出　　处：《数学的实践与认识》2023年第12期243-250,共8页Mathematics in Practice and Theory

基　　金：陕西省一流课程建设项目《常微分方程》(2020-156);陕西省科技厅研究项目(2022JM-050);陕西省教育科学研究项目(SGH22Y1458)。

摘　　要：在现代科学中,Burgers方程模型在物理和通信技术等领域有着重要的地位和作用.一种可行方法是将Burgers方程转化为Riccati方程或二阶线性微分方程探讨其解.但由于Riccati方程的不可积性,使其求解异常困难.现利用Riccati方程的不变量关系,统一给出相关文献中关于Burgers方程的Riccati方程解形式,形成统一的解理论.In modern science,Burgers equation model plays an important role in the fields of physics and communication technology.A feasible method is to transform Burgers equation into Riccati equation or second-order linear differential equation to explore its solution However,due to the non integrability of Riccati equation,it is very difficult to solve it.Using the invariant relation of Riccati equation,the solution form of Riccati equation about Burgers equation in relevant literature is given.

关 键 词：BURGERS方程 RICCATI方程 精确解 不变量 

分 类 号：O175[理学—数学]