1) first integral method
首次积分法
1.
With the aid of computer symbolic systems Maple,and by the first integral method which is to obtain a series of exact solutions to some nonlinear differential equation,we have solved the Burgers-Huxley equation,and obtained a number of new exact solutions including solutions with arbitrary constant,soliton-like solutions and implicit solutions.
借助符号计算软件Maple,运用首次积分法求解Burgers-Huxley方程,得到该方程一系列新的精确解,包括含有任意参数的解、类孤立波解以及隐式解。
2.
Applying a new method called the first integral method,we obtain some exact solutions of a kind of reaction diffusion equations u_t-u_(xx)+αu+βu~2+γu~3=0.
运用首次积分法并借助计算机符号计算系统Mathematica得到了一类非线性反应扩散方程u_t-u_(xx)+au+βu~2+γu~3=0的精确解,其中既包括已知的类孤立波解,又有新的精确解。
3.
Given a different method for the proving the Cauchy mean-value theorem by using first integral method to construct assistant functions and in weakened or enhanced condition,get a symmetry result which is a extension of the Cauchy mean-value theorem.
通过首次积分法构造辅助函数,给出了Cauchy中值定理的另一种证明思路。
2) initial integral method
首次积分法
1.
The paper constructs an auxiliary function by using initial integral methodo,ffers a new method to prove Lagrange’s mean-value theorem and Cauchy’s mean-value theoremf,inds several conclusions in the application of differential mean-value theorem.
通过首次积分法构造辅助函数,给出了Lagrange中值定理和Cauchy中值定理的另一种证明思路,得到了微分学应用中的几个结果。
2.
The paper constructed an auxiliary function by using initial integral method,offered a new method to prove Lagrange s mean-value theorem and found several conclusions in the application of differential calculus.
通过首次积分法构造辅助函数,给出了Lagrange中值定理的另一种证明思路,得到微分学应用中的几个结论。
3) first integral
首次积分法
1.
Based on the method of first integral,the problems of constructing functions,such as the differential mid-value theorem,the solution of integrating factor and thr zero existence of some functions,are explored.
基于首次积分法,对微分中值定理中的辅助函数、求解积分因子、函数零点存在等中的函数构造问题作了探讨,从而构造辅助函数转化为求首次积分,易于操作,且用实例解释其合理性。
4) first integral
首次积分
1.
Let x~2+y~2+z~2=h(>0) be the first integral of the perturbed system,then the existence of limit cycles on the spherical surface was discussed by using averaging method and center manifold theory.
对球面族上的平行流进行了一般的2n+1次齐次扰动,在x2+y2+z2=h(>0)是扰动系统的首次积分的情况下,运用平均方法及中心流形定理,给出了扰动系统在球面上出现极限环的一般情况。
2.
Under general conditions, a method for solving first integrals of the 3-rd order autonomous system is given based on the generators of two admitted single-parameter Lie groups.
在较一般的条件下,对3阶自治系统给出利用系统所接受的两个单参数李群的生成元计算首次积分的方法。
5) First integrals
首次积分
1.
Two first integrals for the Helmholtz oscillator
Helmholtz振荡系统的首次积分
2.
Darboux polynomials and first integrals have close relation,the conditions for the existence of a Darboux polynomial are much weaker than the conditions for the existence of a fist integral,it is positive meaning that we use Darboux polynomials to find out first integrals of the polynomial system or use the nonexistence of Darboux polynomials to prove the nonexistence of first integrals.
达布多项式与首次积分有密切联系,而且达布多项式存在性条件比首次积分存在性条件弱得多,故利用达布多项式寻找多项式系统的首次积分(或由达布多项式的不存在性证明首次积分的不存在性)有积极意义。
6) quadratic first integral
二次型首次积分
补充资料：首次积分
首次积分
first integral
首次积分沛仗i画花邝l;nep肠‘妞。Terpa。]，常微分方程的，亦称第一积分 不为常数的连续可微函数，其导数沿给定方程的解恒等于零.对于标量方程 夕’=f(x，夕)，(*)在通解F(x，y)=C(C为任意常数)中出现的函数F(x，y)是一个首次积分.所以，F(x，y)满足含一阶偏导数的线性方程 刁尸(x，夕).日F(x，夕)，，.、_。 二二止二乙乙2二+一f(x，y)=0. 口x’日y首次积分在方程(*)的整个定义域内可能不存在，但是在使得函数f(x，y)连续可微的点的邻域内必定存在.首次积分不是唯一确定的.例如，对于方程y’=一x/夕，不仅函数扩十尹是首次积分，而且函数exP(x，+y，)等也是首次积分. 知道了正规方程组 又=f(x，r)，x6R”的一个首次积分，就能把这个方程组降低一阶，求n个函数无关的首次积分等价于求隐形式的通解.如果F.(x，t)，…，凡(x，t)是”个函数无关的首次积分，则任何其他首次积分F(x，t)都能写成下列形式: F(x，r)=中(F】(x，t)，…，凡(x，r))，其中小是某个可微函数.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条