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1)  one-soliton solution
1-孤子解
1.
The known one-soliton solution in a simple parametric form is obtained by using the scattering data.
首先利用反散射方法建立了DGH方程的反散射方程以及一系列求解方程,并且给出了解的一般形式,然后利用散射数据以参数形式给出了DGH方程的1-孤子解,最后画出了几个取特殊值时解的侧面图。
2)  1-Soliton
1-孤子
3)  soliton solution
孤立子解
1.
Sufficient conditions for the shorter curve of soliton solutions of KdV equations;
一类孤立子解为短程线的充分条件
2.
Multi-soliton solution of the Faddeev model;
Faddeev模型中的多孤立子解
3.
Exact travelling wave solutions and concave or convex peaked and smooth soliton solutions of Camassa-Holm equation;
Camassa-Holm方程的精确行波解及其凹凸尖峰与光滑孤立子解
4)  multi-soliton solutions
多孤子解
1.
Novel multi-soliton solutions of the breaking soliton equation;
(2+1)维破裂孤子方程的新多孤子解
2.
Bcklund transformation of Burgers equation by the improved homogeneous balance method was pushed out,To the above effect,general formal exact solutions,multi-soliton solutions were obtained,with thr.
推导方程的Bcklund变换是齐次平衡法一个重要应用,利用改进的齐次平衡法推导出Burgers方程的Bcklund变换,进而得到Burgers方程的一般形式的精确解与多孤子解,并列出三种特殊情形的孤子解。
3.
The exact expression of multi-soliton solutions to the KdV-mKdV equation is obtained by Hirota method and the interaction process of multi-soliton is described by numerical figures.
应用Hirota方法得到KdV-mKdV混合方程多孤子解的解析表达式,通过图形展示多孤子相互作用,并且从理论上对孤子解的渐进分析证实孤子的特征。
5)  soliton-like solution
类孤子解
1.
Several exact soliton-like solutions for the variable coefficient KdV equation are obtained through use of the corresponding reduced NLODE.
利用一种函数变换将变系数KdV方程约化为非线性常微分方程(NLODE),并由此NLODE出发获得变系数KdV方程的若干精确类孤子解。
2.
By use of solutions of the auxiliary equation,and through making a function transformation,the new soliton-like solutions and the triangle function wave solutions to some equations are constructed with the help of symbolic computation system Mathematica.
给出一种辅助方程的解,并通过一种函数变换,借助符号计算系统Mathematica构造了两类变系数KdV方程、广义变系数KdV方程和带有强迫项的KdV方程的新的类孤子解和三角函数波解。
3.
Then the solutions of the equations istructureed by more wide assuming, and lastly we get new soliton-like solutions to the Broer-Kaup equations.
本文通过适当变换,将Broer-Kaup方程组变为一个简单的方程,然后利用比较广泛的假设,用Riccati方程的解来构造该方程的解,得到了Broer-Kaup方程组的新类孤子解。
6)  soliton solutions
孤立子解
1.
Peaked soliton solutions of shallow water wave equations on nonlinear strength;
非线性强度下浅水波方程的尖峰孤立子解
2.
Some solutions are obtained which include bright soliton solutions,dark soliton solutions,Jacobi elliptic function doubly periodical solutions,triangular solutions,and a new type of soliton solutions by this method.
将范恩贵教授最近提出的新代数法推广应用到Zakharov方程组,比较方便地得到了新的解析周期解,包括亮孤子解、暗孤子解J、acobi椭圆函数双周期解、三角函数解和一种新形式的孤立子解等。
补充资料:解由
1.宋元时官吏调任时的证明文书。
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