Application of mechanized mathematics to rotor dynamics

Based on the mechanized mathematics and WU Wen-tsun elimination method, using oil film forces of short-bearing model and Muszynska' s dynamic model, the dynamical behavior of rotor- bearing system and its .stability of motion are investigated . As example , the concept of Wu characteristic set and Maple software , whirl parameters of short- bearing model, which is usually solved by the numerical method, are analyzed. At the same time , stability of zero solution of Jeffcott rotor whirl equation and stability of self-excited vibration are studied. The conditions of stable motion are obtained by using theory of nonlinear vibration .     

Pansymmetry and fixed pansystems theorems

In this paper, we continue the research of fixed pansystems theorems presented in ref [1], and discuss the existence, the structure and the number of fixed subsets.     

求解非线性方程的双函数法

基于齐次平衡法和李志斌的tanh函数法,得到简单有效的求解非线性发展方程的双函数法,这种方法利用非线性发展方程孤立波的局部性特点,把非线性方程的孤波解表示为函数f和g的多项式,并用这种方法求出了非线性波理论中的基本模型KdV方程的多组孤波解。     

关于构造数学物理中非线性发展方程组孤波解的一种新算法

根据改进的sine-cosine法和吴文俊消元法,给出了一种构造非线性发展方程组孤波解的新算法。这种算法比已知的双曲函数法有更好的结论,并且在使用的过程中更简单。借助于MATH-EMATICA软件,这一算法能够在计算机上实现。     

一类Burgers-KPP方程新的显式精确行波解

In this paper, many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Petrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method, which include new singular solitary wave solutions and periodic solutions. Particular important cases of the equation, such as the generalized Burgers-Fisher equation, Burgers-Chaffee infante equation and KPP equation, the corresponding solutions can be obtained also. The method can also solve other nonlinear partial differential equations.     

一类非线性演化方程新的行波解

利用双函数法和吴消元法,得到了一类非线性演化方程在不同情况下的一系列显示精确解.Sinh-Gordon方程及Klein-Gordon方程作为该方程的特例也得到了相应的行波解.     

2-齐次多项式集合的吴消元法

1引言 考虑2-齐次多项式集合p,两组变量分别记为x=(x_1…,x_n)与y=(y_1…,y_m),p的零点集Zero(P)为有限点集.利用吴消无法([7],[6])可以将此类多项式集合完全三角化从而求得全部解,但这样消元的复杂度甚高.