linear partial differential Equation

To the double independent real variable linear partial differential equation (system of equations ) , a sufficient condition for the existence of the harmonic function solution is supplied, and a method of how to obtain this harmonic solution under this condition is given.

給出具有兩個實自變數的未知函數的線性偏微分方程（組）調和函數解存在的一個充分條件，及在此條件下方程（組）調和函數解的簡化求法。

Classification of Bcklund transformations among second-order nonlinear partial differential equations;

二階非線性偏微分方程之間Bcklund變換的分類

Based on the Homogeneous Balance Method,four methods to find exact traveling wave solutions of nonlinear partial differential equations are proposed by using trigonometric functions,hyperbolic functions and Mathematica software.

基于齊次平衡法的思想,借助數學軟件"Mathematia",利用三角函數、雙曲函數和吳消元法建立了四種尋找非線性偏微分方程行波解的方法,方法的基本原理是通過一些特殊的變換,將求方程行波解的問題轉化為求代數方程的解問題,并且以復合KdV方程作為例子,介紹了方法及其步驟。

By utilizing the trial function method, a class of nonlinear partial differential equations (PDEs for short) that are hard to be solved by the usual ways can be reduced to a set of algebraic equations, which can be easily solved, and their related coefficients can be easily determined by the undetermined coefficients method.

利用試探函數法,將一個難于求解的非線性偏微分方程化為一個易于求解的代數方程,然后用待定系數法確定相應的常數,簡潔地求得了一類非線性偏微分方程的精確解。

Bifurcations of Travelling Wave Solutions for A Class of Nonlinear Partial Differential Equations

一類非線性偏微分方程行波解的分支

Domain Wall Waves of the Cubic Nonlinear Equation;

一個三階非線性偏微分方程的域墻波

New Exact Solutions of Two Kinds of Nonlinear Partial Differential Equations

兩類非線性偏微分方程的新的精確解

Simulation of Lattice BGK Models for Some Nonlinear Partial Differential Equations

若干非線性偏微分方程的格子BGK模擬

The Miura transformation between nonlinear partial differential equations

非線性偏微分方程之間的Miura變換

A Class of Problem for Determining Solution of Second-order Linear Partial Differential Equations of the Solution of the Problem

一類二階線性偏微分方程的定解問題

RKMK Geometric Integration of Non-linear Partial Differential Equations;

非線性偏微分方程的PKMK型幾何積分方法

The Method of Rational Expansion for Finding Exact Solutions of the Nonlinear Partial Differential Equations;

求非線性偏微分方程精確解的有理展開方法

Application of Invariant Subspace Method to Nonlinear Partial Differential Equations

不變子空間方法在非線性偏微分方程中的應用

Mountain Pass Lemma and Existence of the Solutions for Partial Differential Equations with Asymptotically Linear Property;

山路引理與漸近線性偏微分方程解的存在性

Study on Solving Methods and Properties of Solutions for Several Kinds of Nonlinear PDEs;

幾類非線性偏微分方程解法及解的性質的探討

The Study on the Property and Exact Solutions for Nonlinear Partial Differential Equations;

非線性偏微分方程的Painlevé性質及其精確解的推導

Study on Integrable Properties for Two Kinds of Variable-coefficient Nonlinear Partial Differential Equations;

兩類變系數非線性偏微分方程的可積性質研究

On the Initial-boundary Value Problem for the Nonlinear Partial Differential Equation with Integral Term;

一類具積分項非線性偏微分方程的初邊值問題

Several Finite Difference Schemes for a Family of Nonlinear PDES;

一類非線性偏微分方程的若干有限差分格式

Analysis & Application to Some Methods for Solving Nonlinear Partial Differential Equations;

非線性偏微分方程若干解法分析與應用

Group-invariant Solutions and Group Classification of Nonlinear Partial Differential Equations;

非線性偏微分方程的群不變解和群分類

Applications of Bifurcation Theory in a Semilinear Partial Differential Equations

分歧理論在一類半線性偏微分方程中的應用