THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM

I.IntroductionThemethodofseparationofvariablesisimportanttosolvethesoluti0n0fprobIem0fmathematicalphysics,butmanyproblen1sofmathematicalphysicscannotseparatet'ariab1es,thereforeitrestrictstheranget0appIicatemethodofseparationofvariable.Inthepaperlll,Zhong…     

一个2+1维可积方程的代数几何解

该文从1+1维的孤子方程出发,构造出一个2+1维在Lax意义下可积的方程.接着这个2+1维可积方程被分解为可解的常微分方程.随后引入超椭圆Riemann曲面和Abel-Jacobi坐标把流进行了拉直.再利用Riemannθ函数给出了这个2+1维方程的代数几何解.     

Analytic Solution for Magnetohydrodynamic Stagnation Point Flow towards a Stretching Sheet

A steady two-dimensional magnetohydrodynamic stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The analytic solution is obtained by homotopy analysis method. The convergence region is computed and the feature of the solution is discussed.     

Two new discrete integrable systems

In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.     

The soliton-like solutions to the （2＋1）-dimensional modified dispersive water-wave system

By a simple transformation, we reduce the (2 1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method.     

Generalized Riccati equation expansion method and its application to the Bogoyavlenskii''s generalized breaking soliton equation

Based on the computerized symbolic system Maple and a Riccati equation, a Riccati equation expansion method is presented by a general ansatz. Compared with most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear differential equations. Making use of the method, we study the Bogoyavlenskii's generalized breaking soliton equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions.     

一族Liouville可积系及其约束流的Lax表示、Darboux变换

利用屠规彰格式求出了一族Liouville可积系,通过高阶位势特征函数约束将可积系分解成x部分和t_n部分可积Hamilton系统,求出了该系统的Lax表示及三类Darboux变换。     

判定线性偏微分方程组解的完备性的一个符号计算方法

从微分代数的角度出发,借助于吴微分特征集理论,对于线性偏微分方程组,给出了判定它的解的完备性的一个符号计算方法.这个算法是一个机械化的算法,借助于符号计算软件Maple,可以在计算机上实现.     

Analytic solutions of a class of nonlinear partial differential equations

An approach is presented for computing the adjoint operator vector of a class of nonlinear （that is, partial-nonlinear） operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear （partial-nonlinear and including all linear） and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.     

一类非线性偏微分方程组的解析解

首先,利用共轭算子的性质,将张鸿庆等提出的求伴随算子对的方法推广到了求一类非线性(即部分非线性的)算子矩阵的伴随算子向量．其次,利用机械化的构造方法给出了求解一类非线性(即,部分非线性的,且以所有线性的为其特例)非齐次微分方程组的统一理论,即通过齐次化和三角化求得恰当的变换,从而将原方程组化为较简单的形式,一般为对角化的．最后利用该方法求得了一些弹性力学方程组的解析解．