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1)  the modified generalized F-expansion method
广义的扩展F-展开法
2)  generalized modified F-expansion
广义扩展的F-展开法
1.
The generalized modified F-expansion method is developed to solve nonlinear mathematic physic equations.
从解的形式和约束条件两个方面对求解非线性数学物理方程的F-展开法进行了改进,得到广义扩展的F-展开法。
3)  generalized F-expansion method
广义F展开法
1.
By using the white noise analysis,Hermite transform and the generalized F-expansion method,a number of Wick versions of white noise functional solutions,trigonometric function solutions and hyperbolic function solutions for the Wick-type stochastic clannish random walker s parabolic equation and the one with variable coefficients are obtained,respectively.
通过白噪声泛函分析理论、Hermite变换和广义F展开法,分别得到Wick型clannish random walker's para-bolic方程和变系数的clannish walker's parabolic方程的白噪声泛函解、三角函数解及双曲函数解。
4)  extended F-expansion method
扩展F-展开法
1.
By using extended F-expansion method,a number of exact solutions,which are expressed by Jacobi elliptic functions to nonlinear evolutional equations with variable coefficients were found.
利用扩展F-展开法求出了一个变系数非线性演化方程更多个以Jacobi椭圆函数表示的精确解,当模数m→1或m→0时,可得到类孤立波解和三角函数表示的精确解。
2.
By using the extended F-expansion method recently proposed,a number of periodic wave solutions to the nonlinear equation with variable are obtained,which are expressed by Jacobi elliptic functions.
直接利用扩展F-展开法求出了一个变系数非线性演化方程的更多个以Jacobi椭圆函数表示的精确解。
3.
With the coupled Burgers system,this paper deduces a number of solutions expressed by hyperbolic solitary wave function,triangular function and rational function,by applying the extended F-expansion method and Riccati equations.
针对耦合Burgers系统,采用扩展F-展开法和Ricctia方程辅助,通过Maple辅助计算得到了双曲函数扭状孤波解、三角函数周期解和有理函数解。
5)  generalized expansion method
广义展开法
1.
In the paper,by using Hermite tranformation,Wicktype stochastic generalized kdv equation is reduce to stochastic coefficient equation,then some stochastic exact solutions are obtained via generalized expansion method and Hermite inverse transformation.
利用埃尔米特变换求出了Wick-类型的随机广义Kdv方程的精确解,这种方法的基本思想是通过埃尔米特变换把Wick-类型的随机广义Kdv变成广义系数Kdv,利用广义展开法求出方程的精确解,然后通过埃尔米特的逆变换求出方程的精确解。
6)  F-expansion method
F展开法
1.
Solving KdV equation with variable coefficients by using F-expansion method;
用F展开法解变系数KdV方程
2.
The extended F-expansion method and new exact solutions of the generalized KdV equation
修正的F展开法和推广的KdV方程新的孤波解和精确解
3.
The F-expansion method which can be used to solve nonlinear equations has been summarized.
对求解非线性方程的F展开法进行了综述,揭示了方法的内在本质,指出了F展开法可能的发展方向,并结合F展开法的最新进展,给出了一个辅助常微分方程,借助它可求解具有高次非线性项的非线性偏微分方程。
补充资料:上行展开法
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性质:在平面色谱中,溶剂沿纸或薄层板的下端不断地向上移动的展开过程。是最常用的展开法。

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