Benjamin方程的Bcklund变换、非线性叠加公式及无穷守恒律

利用屠格式求出了Benjamin方程的B cklund变换、精确孤波解、非线性叠加公式及其无穷守恒律·　这种算法具有普适性·     

Benjamin方程的Bcklund变换、非线性叠加公式及无穷守恒律

利用屠格式求出了Benjamin方程的Bcklund变换、精确孤波解、非线性叠加公式及其无穷守恒律.     

一类微分差分方程的无穷守恒律及Backlund变换

In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given for- mularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.     

广义Heisenberg方程的无穷守恒律

本文给出了Heisenberg方程的无穷守恒律,并具体给出了其前三个守恒律,特别得到了铁磁链方程无穷多个微分形式与积分形式的守恒律。     

非线性对流扩散方程的守恒律

利用直接方法研究了非线性对流扩散方程的守恒律,得到了关于非线性对流扩散方程的守恒律乘子性质的一个定理.利用这个定理,可以简化守恒律乘子的确定方程.随后通过对确定方程中的变量函数进行分析,发现在四种情况下乘子的确定方程是可解的.最后解出这些守恒律乘子,利用积分公式法分别得到了四种情况下对应于各个守恒律乘子的守恒律.     

非线性耗散方程的Baecklund变换及对称约化

应用齐次平衡法思想，求出非线性耗散项的Burgers-Fisher方程Baecklund变换，若干对称约化和相似解。     

一个离散晶格方程的N波Darboux变换和无穷守恒律

根据已知离散晶格方程的Lax对,构建了该方程的Ⅳ波Darboux变换和无穷守恒律,通过应用Darboux变换,得到离散晶格方程的范德蒙行列式形式的精确解,通过画图给出了该方程一类特殊的单孤子结构.     

Modified Boussinesq方程的一种Darboux变换和守恒律

利用Modified Boussinesq方程的Lax对,为该方程建立了一种简单的没有约束条件的Darboux变换,并给出了证明.基于3×3矩阵Lax对,构造了Modified Boussinesq方程的无穷多守恒律.     

非线性扩散方程和Thompson方程的无穷维Lie代数(英文)

本文研究非线性扩散方程(1.1)和Thompson方程(2.1)的对称结构,提出了一种产生无穷维Lie代数的简单途径:仅从递推算子的基本关系式出发,无须进行Frechet导数的冗长计算就可得到某种“抽象”的仿射Lie代数。通常经由Frechet导数产生的Lie代数只是上述的仿射Lie代数的具体实现。     

非线性变换和守恒律方程的非自相似解

该文提出了一种非线性变换把一类n维单守恒律方程和初值同时降维为一维, 得到非自相似形式的全局解和基本波的表达式，并发现了非自相似解和相似解之间的本质性差别和联系     

Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation

Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers.     

变量变换和几类里卡提方程的通解

研究了几类里卡提方程,利用变量变换法将其化为伯努利方程或可分离变量微分方程,从而求出方程的通解,还得到方程的一个特解.并给出了几个例子来验证主要结论.     

变量代换法和几类阿贝尔型方程的通解

研究了几类阿贝尔型方程,利用变量代换法得到了方程的通解的充分性条件.     

Algebraic and Differential Nonlinear Superposition Formulas

Knowledge of the Lax pair and the Darboux transformation for a completely integrable system provides an iterative approach for generating exact solutions. This approach involves solving for the eigenfunction of the Lax pair at each step. But this process can be considerably simplified using the Bäcklund transformation and Bianchi's permutability theorem. This allows constructing the so-called nonlinear superposition formula, which provides a new solution of the system in terms of three previous solutions. The advantage of this approach is that the differential order of the nonlinear superposition formulas is lower than that of the Lax pairs, and in some cases, these formulas reduce to algebraic equations. We consider the construction of new nonlinear superposition formulas in the form of both differential equations and algebraic equations.     

Tracking the Solution to a Nonlinear Distributed Differential Equation by Feedback Laws

In this paper, a nonlinear distributed second order equation is considered. An algorithm for tracking a prescribed solution based on constructions of feedback control theory is designed. The algorithm is stable with respect to information noise and computation errors. It is designed for solutions in a sufficiently large time interval.     

Hill's Equation Systems and Infinite Determinants

In this paper a method is developed to calculate the Floquet exponents of the matrix-valued version of Hill's equation using infinite determinants. It is shown that the Floquet exponents are precisely the zeros of an infinite determinant corresponding to the differential equation. The proof of this result uses the continuity and holomorphy of the infinite determinant.