1) Hirota's direct method
Hirota直接方法
1.
In this paper, we discuss mainly three aspects about the Hirota's direct method, perturbation, symmetries and similarity solutions of nonlinear partial differential equations, and they read as follows: 1.
本文围绕孤子理论的Hirota直接方法，扰动，对称，相似解等问题做了以下三方面的主要工作： 1、首先研究了双线性算子的一些性质，得到了在对数变换意义下KdV类的双线性方程所直接相对应的非线性pde(即过渡方程)的一些性质。
2) Hirota method
Hirota方法
1.
Solving the Boussinesq equation by the Hirota method;
Hirota方法求解Boussinesq方程
2.
The mu liti-so liton solution of KP equation by Hirota method;
Hirota方法求解KP方程的多孤子解
3.
The new periodic wave solution for the(2+1)-dimensional Boussinesq equation is presented by using of Hirota method and Riemann theta function,from which the soliton solution can be obtained via an appropriate limited procedure.
利用Hirota方法及Riemanntheta函数得到了(2+1)维Boussinesq方程的新的周期解。
3) Hirota bilinear method
Hirota双线性方法
1.
Using the Hirota bilinear method,N-soliton solution is obtained for a (2+1)-dimensional nonlinear evolution equation,utt-uxx-uyy-3(u2)xx-uxxxx=0.
研究了一个2 +1维变形Boussinesq非线性发展方程:utt-uxx-uyy-3(u2)xx-uxxxx=0,运用Hirota双线性方法得到它的N孤子解。
2.
In this thesis, based on the Hirota bilinear method, we mainly discuss how to solve various forms of exact solutions.
本论文就是基于Hirota双线性方法来求解孤子方程的各种精确解并构造两类可积偶合系统。
3.
For example,Hirota bilinear method and Wronskian technique are two important tools to deal with soliton problems.
Hirota双线性方法和Wronskian技巧是两种比较常见的求解方法。
4) Direct Method
直接方法
1.
Optimization of adaptive direct methods of Fredholm integral equations of several variables;
多元Fredholm积分方程自适应直接方法的优化
2.
The Important Role of Direct Method of Social Work in FP Work at Grassroot Level;
试论社会工作直接方法在计划生育基层工作中的重要作用
3.
The practical stability in terms of two measures of impulsive differential systems and its perturbed systems is de-veloped by Lyapunov direct method.
运用李雅普诺夫直接方法研究了脉冲微分系统及其摄动系统关于两个测度的实际稳定性。
5) direct methods
直接方法
1.
The optimization of direct methods and information complexity for approximate solution of operator equation are two main aspects of information-based complexity theory, which has been developed from the eighties and is an interdiscipline of computer science and mathematics.
算子方程近似解直接方法的优化和信息复杂性是80年代发展起来的连续复杂性理论的两个主要方面,是计算机科学和数学的交叉研究领域。
6) Hirota equation
Hirota方程
1.
In this paper, we consider the dynamical behavior for some nonlinear evolution equations, such as Long-Short wave equations, Hasegawa-Mima equation and Hirota equation.
本文研究了长短波方程组、Hasegawa-Mima方程和Hirota方程等非线性发展方程的周期边值问题或初值问题的动力学行为，得到了相应问题整体解的存在性、整体吸引子的存在性及其分形维数的有限性估计，构造了相应问题的近似惯性流形。
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