三分子反应模型无代数曲线解  

Non-Algebraicity of the Solution Curves of the Trimolecule Reaction Model

作　　者：李林[1] 

机构地区：[1]北京石油化工学院,北京102600

出　　处：《石油化工高等学校学报》2000年第3期73-77,共5页Journal of Petrochemical Universities

摘　　要：对于二维微分方程组 ,如果它的解轨线是代数曲线或其一枝 ,则称该二维微分方程组有代数曲线解。对一类多项式微分系统dx/dt=A -y ,dy/dt =b0 ( y) +b1( y)x的代数曲线解的存在性 ,通过具体的分析运算得出该多项式微分系统存在代数曲线解的充分必要条件为一组具有递推性的线性微分方程组具有多项式解。所得结果用于著名的Pigogine三分子反应模型时 ,在假定对应的线性微分方程组有多项式解的情况下 ,得到矛盾 ,从而证明该三分子反应模型无代数曲线解。For a 2-dimensional differential equations, if its trajectories are algebraic curves or some of their branches, then it is called to have algebraic curve solutions. The existence of algebraic curve solutions of a polynomial differential system d x /d t=A-y , d y /d t=b 0(y)+b 1(y)x is studied. By some analytic calculation, it is proved that the polynomical differential systems has algebraic curve solutions if and only if a linear differential equations with finits iterative scheme has a polynomial solution. For the famous prigogine trimolecule reaction model, by solving the linear differential equations corresponding to the model, it can be seen that the model has not any polynomial solutions. Therefore, the non-algebraicity of the solution curves of the trimolecule reaction model is showed.

关 键 词：三分子反应模型 代数曲线解 微分方程组 

分 类 号：O241.8[理学—计算数学] O175[理学—数学]