非线性演化方程

显然，扩展的F展开方法也可以解其他类型的非线性演化方程。

Obviously , the extended F-expansion method can be applied to solve other type of nonlinear evolution equations as well .

Lam函数和非线性演化方程的多级准确解的不变性

Lam è function and invariants of multi-order exact solutions among nonlinear evolution equations

用齐次平衡原则和辅助微分方程方法得到了6个重要的n次非线性演化方程的孤立波解。

The solitary wave solutions for six important nonlinear evolution equations with n degree nonlinearity are obtained by the homogeneous balance principle and sub-ODE method ( mean by subsidiary ordinary differential equation method ) .

借助Maple软件，采用吴方法及改进的齐次平衡法，研究了一类非线性演化方程的精确行波解。

With the help of software Maple , Wu 's method and Improved Homogeneous Balance Method are used to study exact traveling solutions of a kind of nonlinear evolution equation .

推广了Jacobi椭圆函数展开方法，研究了复非线性演化方程组的求解问题，得到了长短波相互作用方程的准确包络周期解。

In this paper , the Jacobi elliptic function method is generalized to study nonlinear evolution system . The envelope periodic solutions of long-short wave interaction equation are obtained .

通过选取恰当修正项，由零曲率方程获得一族新的Lax可积系，作为其约化情形，得到了一类耦合非线性演化方程。

By choosing proper modified terms , a new Lax integrable system is presented via the use of zero-curvature equation . As its reduction , a coupled nonlinear evolution equation is followed .

导出了磁绝缘传输线振荡器（MILO）中辐射场的非线性演化方程，并讨论了在临界值点附近可能出现非线性不稳定解的条件。

A nonlinear evolution equation for the radiation field in magnetically insulated transmission line oscillator ( MILO ) is derived and the threshold conditions of the nonlinear unstable solution are studied .

许多新的寻找非线性演化方程的精确解的方法被提出，如齐次平衡法、试探函数法、双曲正切函数法、sine-cosine法以及Jacobi椭圆函数展开法等。

Many new methods for obtaining the exact solutions of NLEEs are proposed , such as the homogeneous balance method , the trial function method , the tanh-function method , the sine-cosine method and Jacobi elliptic function expansion method , etc.

一类非线性演化方程的孤子微扰理论

Soliton Perturbation Theory for a Sort of Nonlinear Evolution Equations

非线性演化方程的对称性和守恒律之间的关系

Relationship between symmetries and conservation laws of Nonlinear Evolution Equations

这个方法也可以被应用到其他的非线性演化方程。

This approach can also be applied to other nonlinear evolution equations .

非线性演化方程的多级精确解和周期解

The Multi-order Exact Solutions and Periodic Solutions to the Nonlinear Evolution Equations

与负常曲率曲面相关的非线性演化方程

Non & linear evolution equations related to surfaces of negative constant Curvature

上述非线性演化方程利用半隐傅立叶频域法求解。

The nonlinear evolution equations were solved by a semi-implicit Fourier-spectral scheme .

最后展望了非线性演化方程的研究前景。

Finally , looks forward to the research prospects of nonlinear evolution equations .

非线性演化方程族的零曲率表示

Zero curvature representation for hierarchies of nonlinear evolution equations

函数变换及非线性演化方程的精确解

Function Transformation and Exact Solutions for Nonlinear Evolution Equation

光学孤子在单模光纤中的非线性演化方程

Nonlinear Evolution Equation of Soliton in Single Mode Fiber

任意变系数微分方程的精确解析法一类非线性演化方程的精确解析解

Exact Analytic Method for Solving Variable Coefficient Differential Equation

忒塔函数在求解非线性演化方程中的应用

Application of theta functions for solving nonlinear evolution equations

寻找非线性演化方程精确解的新的双曲函数法

A new hyperbolic functions method for finding exact solutions of nonlinear partial differential equations

在第四章里，首次提出一种形式同一法，并且对一些非线性演化方程进行分类。

In the forth chapter , we propose a unified form method for the first time .

固体中冲击波及其一维一阶非线性演化方程数值模拟

Shock Waves in Solid Medium and Numerical Solutions of its One-Dimensional and First-Order Nonlinear Evolution Equations

一类高维耦合的非线性演化方程的简单求解

A simple method for solving a class of nonlinearly coupled evolution equations in higher dimensional space

本文提出了寻求非线性演化方程的对偶算子的待定系数法。

This paper deals with the dual Toeplitz operators on the orthogonal complement of the Fock space .

求矩阵广义逆的另一种初等变换方法可用逆散射方法求解的一类非线性演化方程

A Solution on General Inverse Matrix A Class of Nonlinear Evolution Equations Solvable by Inverse Scattering Method

近年来，符号计算的蓬勃发展，极大地推动了非线性演化方程的研究。

In recent years , the development of symbolic computation accelerates the research of nonlinear evolution equation greatly .

因此，很多非线性演化方程都与曲线和曲面运动有着密切的关系。

So many nonlinear evolution equations have been shown to be closely related to motions of curves and surfaces .

本文系统地、全面地研究了一类重要的非线性演化方程的孤子微扰问题。

In this thesis , we study systematically and allsidedly soliton perturbation theory for a sort of nonlinear evolution equations .

探究非线性演化方程的解及其性质，对非线性科学的发展意义重大。

Exploring the solutions of nonlinear evolution equations and its properties is of great significance to the development of nonlinear science .