基本解释：线性偏微分方程
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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.给出具有两个实自变数的未知函数的线性偏微分方程（组）调和函数解存在的一个充分条件，及在此条件下方程（组）调和函数解的简化求法。
Classification of Bcklund transformations among second-order nonlinear partial differential equations;二阶非线性偏微分方程之间Bcklund变换的分类
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.基于齐次平衡法的思想,借助数学软件"Mathematia",利用三角函数、双曲函数和吴消元法建立了四种寻找非线性偏微分方程行波解的方法,方法的基本原理是通过一些特殊的变换,将求方程行波解的问题转化为求代数方程的解问题,并且以复合KdV方程作为例子,介绍了方法及其步骤。
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.利用试探函数法,将一个难于求解的非线性偏微分方程化为一个易于求解的代数方程,然后用待定系数法确定相应的常数,简洁地求得了一类非线性偏微分方程的精确解。
Bifurcations of Travelling Wave Solutions for A Class of Nonlinear Partial Differential Equations一类非线性偏微分方程行波解的分支
Domain Wall Waves of the Cubic Nonlinear Equation;一个三阶非线性偏微分方程的域墙波
New Exact Solutions of Two Kinds of Nonlinear Partial Differential Equations两类非线性偏微分方程的新的精确解
Simulation of Lattice BGK Models for Some Nonlinear Partial Differential Equations若干非线性偏微分方程的格子BGK模拟
The Miura transformation between nonlinear partial differential equations非线性偏微分方程之间的Miura变换
A Class of Problem for Determining Solution of Second-order Linear Partial Differential Equations of the Solution of the Problem一类二阶线性偏微分方程的定解问题
RKMK Geometric Integration of Non-linear Partial Differential Equations;非线性偏微分方程的PKMK型几何积分方法
The Method of Rational Expansion for Finding Exact Solutions of the Nonlinear Partial Differential Equations;求非线性偏微分方程精确解的有理展开方法
Application of Invariant Subspace Method to Nonlinear Partial Differential Equations不变子空间方法在非线性偏微分方程中的应用
Mountain Pass Lemma and Existence of the Solutions for Partial Differential Equations with Asymptotically Linear Property;山路引理与渐近线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;几类非线性偏微分方程解法及解的性质的探讨
The Study on the Property and Exact Solutions for Nonlinear Partial Differential Equations;非线性偏微分方程的Painlevé性质及其精确解的推导
Study on Integrable Properties for Two Kinds of Variable-coefficient Nonlinear Partial Differential Equations;两类变系数非线性偏微分方程的可积性质研究
On the Initial-boundary Value Problem for the Nonlinear Partial Differential Equation with Integral Term;一类具积分项非线性偏微分方程的初边值问题
Several Finite Difference Schemes for a Family of Nonlinear PDES;一类非线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;非线性偏微分方程若干解法分析与应用
Group-invariant Solutions and Group Classification of Nonlinear Partial Differential Equations;非线性偏微分方程的群不变解和群分类
Applications of Bifurcation Theory in a Semilinear Partial Differential Equations分歧理论在一类半线性偏微分方程中的应用
