2+1 维变系数广义KP方程的椭圆周期解

运用Jacobi椭圆函数展开法求得了2 1维变系数广义KadoratsevPetviashvili方程的椭圆周期解及孤立波解．     

求Nizhnik-Novikov-Veselov方程新精确解

引入改进的F-广义方法,并将其应用于（2＋1）维Nizhnik-Novikov-Veselov（NNV）方程.在符号计算软件的帮助下,可以得到NNV方程的许多新解.该方法用于获取包括雅可比椭圆函数解的一系列解,在数学物理中可应用于其他的非线性偏微分方程.     

Periodic solutions of the differential delay equation\dot x(t) = - f(x(t - 1))

For an odd function 1/2(x) defined only on a finite interval, this paper deals with the existence of periodic solutions and the number of simple periodic solutions of the differential delay equation (DDE) . By use of the method of qualitative analysis combined with the constructing of special solutions a series of interesting results are obtained on these problems.Supported by the National Natural Science Foundation of China.     

耦合Schr(o)dinger-Boussinesq方程组的显式精确解

本文针对耦合Schrodinger-Boussinesq方程组，借助于F-展开法得到了用不同Jacobi椭圆函数表示的一系列周期波解．在极限情况下，还求出了对应的孤立波解．     

The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)

We determine all the complex polynomials f(X) such that, for two suitable distinct, nonconstant rational functions g(t) and h(t), the equality f(g(t)) = f(h(t)) holds. This extends former results of Tverberg, and is a contribution to the more general question of determining the polynomials f(X) over a number field K such that f(X) – has at least two distinct K-rational roots for infinitely many K.     

Klein-Gordon-Zakharov方程组的周期波解

通过使用符号计算系统Mathematica,并借助于推广的F-展开法,我们得到了Klein- Gordon-Zakharov方程组的用不同Jacobi椭圆函数表示的一系列周期波解．在极限情况下,还求出了对应的孤立波解．     

New Jacobi elliptic functions solutions for the variable-coefficient mKdV equation

In this work, a new generalized Jacobi elliptic functions expansion method based upon four new Jacobi elliptic functions is described and abundant new Jacobi-like elliptic functions solutions for the variable-coefficient mKdV equation are obtained by using this method, some of these solutions are degenerated to solitary-like solutions and triangular-like functions solutions in the limit cases when the modulus of the Jacobi elliptic functions m→1 or 0, which shows that the new method can be also used to solve other nonlinear partial differential equations in mathematical physics.     

具复杂偏差变元的二阶中立型泛函微分方程的周期解

利用拓扑度理论研究了一类具有复杂偏差变元的中立型泛函微分方程的周期解的存在性,得出了周期解存在的充分条件.     

关于函数方程f1n1+af1m1f2m2+f2n2=1

对于函数方程f1n1+af1m1f2m2+f2n2=1,其中a∈C/{0},n1,n2,m1,m2∈N,给出存在非常数亚纯函数解和整函数解的必要条件.     

Periodic solutions of an iterative functional differential equation with variable coefficients

In this paper, we use Krasnoselskii's fixed point theorem to study the existence and uniqueness of periodic solutions of an iterative functional differential equation Copyright © 2016 John Wiley & Sons, Ltd.     

具无穷时滞高阶中立型微分方程的周期解

利用重合度理论研究了一类具有无穷时滞高阶中立型泛函微分方程周期解的存在性,获得了该方程存在周期解的充分条件,推广和改进了二阶方程的相应结果.     

函数方程fn1+afm1fm2+fn2=1的整函数解

对函数方程fn1 afm1fm2 fn2=1,其中a∈C/{0},n,m∈N,给出所有可能的非常数整函数解的形式.     

Soliton and Periodic Wave Solutions of the Nonlinear Loaded (3+1)-Dimensional Version of the Benjamin-Ono Equation by Functional Variable Method

In this article, we establish new travelling wave solutions for the nonlinear loaded (3+1)-dimensional version of the Benjamin-Ono equation by the functional variable method. The performance of this method is reliable and effective and the method provides the exact solitary wave solutions and periodic wave solutions. The solution procedure is very simple and the traveling wave solutions are expressed by hyperbolic functions and trigonometric functions. After visualizing the graphs of the soliton solutions and the periodic wave solutions, the use of distinct values of random parameters is demonstrated to better understand their physical features. It has been shown that the method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.     

(2+1)维modified Zakharov-Kuznetsov方程的复合型新解

给出函数变换,变量分离形式解与第一种椭圆方程相结合的方法,构造了(2+1)维modified Zakharov-Kuznetsov(m ZK)方程的多种复合型新解.步骤一,给出两种函数变换,将(2+1)维m ZK方程转化为能够获得变量分离解的非线性发展方程.步骤二,给出非线性发展方程的变量分离形式解,通过第一种椭圆方程及其相关结论,构造了(2+1)维m ZK方程的双孤子解和双周期解等复合型新解.     

关于指数型超椭圆方程x^2=p^2m-p^m＋n＋1

证明了指数型超椭圆方程x^2=p^2m-p^m＋n＋1无解（x,p,m,n）,其中x,m,n∈N^＋,m〉n〉1,p∈P．上述结果部分解决了组合论中关于可逆Abel差集的Ma猜想．     

On the completeness of the normal solutions of the equation Au′(t) + Bu(t) = f(t)

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 48, pp. 46–51, 1987.     

Periodic solutions of a 2nth-order nonlinear difference equation

In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Results obtained complement or improve the existing ones.