特别是说明了投影算子与孤子解之间的联系。
Especially indicate the relation between projection operation and the soliton solution.
本文利用齐次平衡法并借助数学给出它新的多孤子解。
In this paper, by using the homogeneous balance method and Mathematica, we have obtained new multisoliton solutions of this equations.
用逆散射方法，得到了含时外磁场驱动下一维自旋链的N孤子解。
Exact N-soliton trains in a spin chain driven by a time-dependent magnetic field are obtained by means of an inverse scattering transformation.
本文用参量变换法直接导出了有耗光纤的孤波方程及其基态孤子解。
In this pater, using parametric transform method direct derive soliton wave equation of loss optical fibers and elementary soliton solution.
形式变量分离方法是寻找非线性物理方程孤子解的一种行之有效的方法。
The formally variable separation approach is one of the best method to looking for the exact solitary wave solutions of a nonlinear physical model.
使用齐次平衡方法，得到了（2+1）维破裂孤子方程的一些新多孤子解。
Using the extension homogeneous balance method, we have obtain some new special types of soliton solutions of the (2 + 1) - dimensional breaking soliton equation.
利用该方法，运用计算机符号计算，求出了变系数的一般浅水波方程的孤子解。
In this paper, based on the computerized symbolic computation, solutions of variable-coefficient the generalized shallow water wave equation are obtained.
第一章，简要介绍非对易的概念及非对易场论，回顾前人在非对易孤子解方面的研究。
In Chapter 1, briefly introduce the concept of noncommutative space and nori-commutative field theory, review the history and important results of studying the noncommutative soliton solution.
第五章我们运用小幅度近似方法求解高阶非线性薛定谔方程，得出了它的亮、暗孤子解。
We solve the higher order nonlinear Schrodinger equation by means of the small amplitude approximate method and present the bright and dark solitons solutions in chapter 5.
结果表明，KP方程允许存在左行孤子、右行孤子、静态孤子解和左、右行孤子的相互作用解。
Thus it can be seen that there exist the soliton solutions of the KP equation running to left and right as well as static and the interaction solutions between left running and right running solitons.
其中达布变换是一种十分有效的方法，它能够从孤子方程的一个平凡解出发求出一系列孤子解。
Among the various approaches, the Darboux transformation is a very powerful tool for constructing soliton solutions of the NLEEs from a trivial seed.
更多。同时在求解过程中略去了将齐次方程分块和双线性化的过程，这样就避免了不适当的分块可能产生的对于模型孤子解的结构的限制。
This extended procedure skips the process of equation splitting and bilinearization so as to avoid the possibility of introducing additional limitation on the structure of the soliton solutions.
通过数值方法直接求解非线性薛定格方程以及变分法近似求出了束缚于一个“凹槽”中的单个空间光孤子解，这种光孤子的存在没有阈值范围，且总是稳定传输的。
By means of the variational approximation and direct simulations we demonstrate the one-soliton state trapped in a channel has no existence threshold and is always stable.
对齐次平衡法的一些关键步骤进行拓宽，获得了一系列非线性方程的多孤子解，使得对非线性方程的多孤子解的求解方法更加直接，且许多步骤可以利用计算机完成。
In this paper we improve some key steps in the homogeneous balance method, then by using this method we are able to obtain multiple soliton solutions of some nonlinear partial differential equations.
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。
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.
AKNS方程是重要的孤子方程，寻找孤立子解的方法往往在该方程上加以验证。
The AKNS equation is an important soliton equation and many methods for soliton solutions are verified by it.
本文主要是用非线性化方法来研究困难的（2+1）维孤子方程的显式的有限参数解的。
The purpose of the present paper is using the nonlinearization approach to study the explicit finite-parameter solution to the difficult (2+1) dimensional soliton equation.
本文获得了增益色散和增益饱和非线性介质中的光孤子脉冲的解析解。
An analytical solution is obtained for soliton pulse propagation in nonlinear media with gain saturation and gain dispersion in this paper.
本文得到考虑了色散项后的一维分子晶体模型的孤子激发的运动解。
A moving solution for soliton excitation of a one-dimensional molecular-crystal model with the dispersion term is found.
得到了非线性系数以及特征长度和预倾角的关系，并且给出了强非局域性的非线性薛定谔方程，最终得到了单孤子和临界功率的解析解。
Then the Schrdinger-type nonlinear equation in strong nonlocality was given and from the equation the analytical expressions of the single soliton and the critical power .
通过数值解孤子方程发现，灰屏蔽孤子诱导的波导在任意光强比率下均为单模。
Solving the soliton equation numerically, we find that waveguides induced by grey screening solitons are always single mode for all intensity rations.
利用孤子波的数学理论到圆截面直筒油管的应力波传播的研究，得出了这类应力波具有孤子波的性质，并导出了它的解的表示式。这对研究弹性圆管应力传输问题是有帮助的。
Using the mathematical theory of soliton wave to study the stress wave of an oil pipe, we show that it has the property of soliton wave and obtain an expression of its solution.
利用孤子波的数学理论到圆截面直筒油管的应力波传播的研究，得出了这类应力波具有孤子波的性质，并导出了它的解的表示式。这对研究弹性圆管应力传输问题是有帮助的。
Using the mathematical theory of soliton wave to study the stress wave of an oil pipe, we show that it has the property of soliton wave and obtain an expression of its solution.
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