The exact solutions of the model are obtained conveniently.
关于这一力学模型得到了简洁明了的精确解。
In this paper, the new exact solutions of (3 + 1) dimensional nonlinear equations are studied.
研究了(3 +1)维非线性方程新的精确解。
By this way, the exact solutions of parabolic lossless nonuniform transmission line can be gained.
用这种等效方法可以求解抛物线型非均匀线的精确解。
By using a mapping method, we obtain exact solutions of the (2 + 1) dimensional long wave equations.
运用数学中的映射方法分析论证，获得了(2 +1)维长波方程组的精确解。
Numerical calculations show that these approximate solutions are in good agreement with exact solutions.
数值计算表明，这些近似解与正确解很好相符。
Some explicit and exact solutions to nonlinear evolution equations were obtained by the (improved) method.
用这种方法和吴消元法，得到一类反应扩散方程的许多显式和精确行波解。
Its symmetry reduction and exact solutions are obtained through the generalized conditional symmetry approach.
通过广义条件对称方法得到了其对称约化和精确解。
The generalized conditional symmetry; Exact solutions; The nonlinear reaction diffusion equations; symmetry group.
广义条件对称；精确解；非线性反应扩散方程；对称群。
Various RATIONAL, polynomials, RATIONAL Exact solutions of equations and transcendental equations and approximate solutions.
进行各种有理式计算，求多项式、有理式方程和超越方程的精确解和近似解。
It is an important method that the exact solutions of the heat conduction equations test the correctness of the numerical solutions.
反之，用数值解来分析精确解的完整性也是一种有意义的方法。
The study of difference equations is main about two problems: exact solutions of the equations and qualitative analysis of the solutions.
差分方程研究的主要内容包括两个问题：差分方程的精确解和方程解的定性分析。
When deconvoluting the signal with noise, there are no exact solutions, so we must use filter to get stable and smooth estimated solutions.
在用带有噪声的信号进行反卷积时，没有严格的解，必须采用滤波器方能得到稳定、平滑的估计解。
Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.
重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。
The exact solutions are analytical physical solutions and can be served as accuracy checks for experimental, numerical and asymptotic methods.
这些精确解为实验，数值以及渐近解的检验提供了借鉴和参考。
In Chapter 6, we study new applications of homogenous balance method and apply the method to WBK equation and obtain many new exact solutions.
第六章研究了齐次平衡法新的应用，把它应用到WBK方程上去得到了许多新的精确解。
Finally, the summary of this dissertation and the prospect of study on constructing exact solutions to nonlinear evolution equations are given.
最后对本文的工作进行了总结，并对今后的研究方向作了展望。
The exact solutions have been found for all configurations with different parameters of shell length, shell thickness, radius and plate thickness.
对于所有给定壳长、壳厚、半径及封头厚的组合结构，均找到了完全解。
Exact solutions to the resulting equations are constructed via the compatibility of the generalized conditional symmetry and the considered equation.
并且依据广义条件对称和所考虑方程的相容性求得了相应方程的群不变解。
The exact solutions to dispersive long-wave equations are obtained by a polynomial expansion method based on the idea of the homogeneous balance method.
基于齐次平衡法的思想，利用多项式展开法解得了具有色散项的长波方程组的精确解。
The exact solutions for a simply supported rectangular thick plate with arbitrary ratio between thickness and width under any given loads are presented.
给出四边简支任意厚宽比的矩形板在任意荷载下的精确解。
The exact solutions of displacement and inner force for clamped rectangular thick plate were deduced with two-dimension finite integral transform method.
利用二维有限积分变换的方法推导出了四边固支矩形厚板位移和内力的精确解。
By using an algebraic method related to su(3) Lie algebra, exact solutions of the eigenvalue problem of the reduced Hamiltonian are derived analytically.
介绍了导出平均场加一般对力核多体问题粒子数守恒严格解的无穷维李代数方法。
A class of exact solutions of the Dirac equation are obtained for an electron in the electromagnetic field of a wave guide formed by two pairs of hyperbolic cylinders.
研究了位于由两对双曲柱面构成的波导管电磁场里的单电子的性质，得到了单电子在场中狄拉克方程的新一类精确解；
This paper takes the NLEEs as a foundation, studies several kinds of significant methods to solve the NLEEs, improves the solution method and find new exact solutions.
本文正是以非线性微分方程的理论为基础，研究了几种重要的求解的方法，并且改进了已经存在的求解方法，求出了新的精确解。
The exact and explicit solutions of these equations are obtained by using the travelling wave method. These exact solutions are solitary wave solutions of a rational type.
用行波方法得到了这些方程的显式精确解，即有理分式型孤立波解。
The exact solutions of a set of non-linear differential equations with limiting conditions describing the anharmonic vibration of a one-dimensional lattice have been obtained.
本文列出了一维点阵非谐振动的非线性微分方程组，并求出了这组方程在相应边值条件下的解析解。
Many of the exact solutions of (3 + 1) dimensional breaking soliton equation are obtained by using a simple transformation relation and solving the ordinary differential equation.
首先通过变换关系和求解简单的常微分方程，得到了(3 +1)维破裂孤子方程丰富的孤立波解和周期波解。
The governing equations as well as their exact solutions are constructed for a simply supported rectangular orthotropic plate with arbitrary thickness subjected to arbitrary Loads.
给出四边简支任意厚宽比的矩形板在任意荷载作用下的控制方程及其精确解。
In this paper, the approximate errors introduced by this method are studied, not only deriving the norm of the errors but also obtaining the bounds in which the exact solutions lie.
本文研究了这种近似解耦方法所引起的近似误差，导出了误差范数，并得到了体系精确解所在范围。
In this paper, the approximate errors introduced by this method are studied, not only deriving the norm of the errors but also obtaining the bounds in which the exact solutions lie.
本文研究了这种近似解耦方法所引起的近似误差，导出了误差范数，并得到了体系精确解所在范围。
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