孤波

The observations of dark and bright matter wave solitons,the study of matter wave solitons have been one of the hot issues in the fields of both low-temperature physics and condensed matter physics due to their potential application.

玻色-爱因斯坦凝聚中的暗，亮物质波孤子的成功观测及它们的潜在的应用前景，也使玻色-爱因斯坦凝聚中的物质波孤子成为了当前低温物理和凝聚态物理研究领域的研究热点之一。

At first,the limitation of the general heat conduction equation is discussed and then,nonlinear heat conduction equations are derived,when we consider that thermal conductivity,specific heat capacity and density are dependent of temperature.

研究了线性情形中热传导方程的局限性，在此基础上考虑到热传导方程中导热系数、比热容、密度与温度的关系，导出了非线性热传导方程，并求出了几类非线性热传导方程的孤波解。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

By means of the undetermined coefficient method ,which is submitted in reference for solving nonlinear wave equations for their peaked soliton solutions ,three kinds of peaked soliton solutions are obtained for two important nonlinear wave equations— Korteweg-de Vries equation and Benjamin-Bona-Mahonyequation,respectively. One kind of peaked compacton solution ,which has the characteristics of both peaked soliton solution and compacton solution ,is obtained for above two equations with the aid of transformation relation between triangle function and hyperbolic function,. By use of above solutions, two kinds of periodic peaked traveling wave solutions are constructed.

摘 要：利用文献中提出的求非线性波方程尖峰孤子解的方法，分别求解了两个重要的非线性波方程—Korteweg-de Vries 方程和Benjamin-Bona-Mahony BBM）方程，得到了3类尖峰孤子解；借助双曲函数与三角函数间的变换关系得到了1类尖峰紧孤子解，该型解兼有尖峰孤子解和紧孤子解的特点；在上述结果的基础上构造了2个周期性的尖峰行波解。

According to the characteristics of peaked soliton solution, the undetermined coefficient method for solving nonlinear wave equations for their peaked soliton solutions is submitted and by means of the method several kinds of peaked soliton solutions are obtained for five nonlinear wave equations: the Camassa-Holm, fifth -order KdV-like, generalized Ostrovsky, combined KdV-mKdV and Klein-Gordon equations.

刘煜 河南电力试验研究院，郑州 450052根据尖峰孤子解的特点，提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法，并利用该方法求解了5个非线性波方程，即CH（Camassa-Holm方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程，比较简便地得到了这些方程的尖峰孤子解。

In this thesis, an unmagnetized, collisionless dusty plasma which consisted of extremely massive, highly negatively charged dust particles, ions and electrons are studied. Considering the effects of hot dust fluid with non-thermal ions and variable dust charge, we study the self-consisted system parameters on the structures of the dust-acoustic solitary waves by reductive perturbation methods.

本论文研究无磁化、无碰撞的、由大质量且带负电量的尘埃颗粒、电子和离子组成的尘埃等离子体，考虑尘埃流体的温度、非热离子和尘埃颗粒电荷绝热变化的因素，使用约化摄动方法研究这个自洽的系统的参数对尘埃声孤波结构的影响。

Fill the bathtup with an inch-deep amount of water, and see if you can produce "solitary" waves.

在浴缸中注入1英寸深的水，然后观察你能否产生孤波（用一定的标准来使水动起来

The repulsions and the energy transferring will are increasing with the varying of the temperature for the -phase-difference solitons.

结果表明：在室温基础上，两个同相位孤子波的相互作用随温度变化伴有融合现象，当温度升高到350K时两孤子可融合成一束稳定的孤子波；两个反相孤子相互排斥现象随温度变化而增强；相位差为的两孤子，其相互作用随温度变化过程中有更多的能量转移，同时两孤子间的排斥现象随温度变化而增强。

According to the self-trapping that takes place in both transversedimensions,we show that an addressing optical switch is possible bychanging the lateral displacement of the beam,that the soliton wavelengthdivision multiplexing devices may be made by using the self-deflection ofspatial solitons,and that soliton devices with two or three controlledparameters are made by using screening-photovoltaic solitons for shortcircuit or closed circuit with an external resistor.

根据光孤子的自陷获仅发生在横向上，由此我们提出：控制横向空间光孤子的方法实现光的快速互连切换光开关；用短路或有外电阻的屏蔽光伏孤子研制具有两种或三种控制参数的孤子器件；用控制空间光孤子的自偏转的方法研制波分复用器。

With reductive perturbation technique, we derived a Korteweg de Vries equation (ut - 6uux + uxxx = 0) of the nonlinear vibrating string equation, which is easier to solve than the original form.

本论文运用约化摄动法分别研究了非线性弦振动、等离子体物理、血液流动和非线性电路传输线等领域中的孤波现象。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷