二阶半线性椭圆方程的径向解

本文讨论了无界域上的二阶半线性椭圆方程的径向解，给出了古典解的性质，诸如存在或非存在性，唯一性以及解的估计式等，这些性质清晰地描绘了古典解的性态。     

第一类不适定算子方程的解的表示

该文在L2中讨论了第一类算子方程Au＝f当A-1无定义和A-1不是单值的情形下的不适定求解问题，给出了解存在的充要条件，当有解时，得到了形式解，多解时形式解就是最小范数解，并且得到了近似解表达式，给出了误差估计．     

Benjamin-Ono方程的广义解

讨论了Benjamin-Ono方程在Colombeau意义下的广义解的存在性，唯一性及在经典解存在的情况下与经典解的关系．     

奇异扰动的p-Laplace方程非负非平凡解和正解的结构

精确地刻画了某些奇异扰动的p-Laplace方程非负非平凡解和正解的结构．利用上下解方法证明，方程存在很多非负非平凡的尖峰解和正的过渡尖峰解．当参数充分小时还对每个尖峰解支集的上下界进行了估计．     

一类非线性方程奇摄动问题的激波解

利用匹配条件，讨论了一类非线性奇摄动问题的激波解，得出了激波解与边界条件的对应关系。     

双函数法及一类非线性发展方程的精确行波解

给出一种求解非线性发展方程精确行波解的新方法：双函数法。使用此方法，获得了一类非线性发展方程的许多精确行波解，其中包括孤波解和周期解，推广了文献用其它方法取得的结果，同时还获得了许多新的弧波解和周期解，借助于Mathemat-ica，此方法能部分地在计算机上实现。     

(2+1)-维广义Benney-Luke方程的精确行波解

用平面动力系统方法研究（2＋1）＋维，“义Benney-Luke方程的精确行波解，获得了该方程的扭波解，不可数无穷多光滑周期波解和某些无界行波解的精确的参数表达式，以及上述解存在的参数条件．     

二维RLW方程和二维SRLW方程的显式精确解

本文讨论了二维RLW方程和二维SRLW方程孤立波解的性态，通过直接积分的方法求出了这两个方程的显式精确孤立波解，并通过选取初始条件的方法求出了二维RLW方程和二维SRLW方程的另一类精确行波解．     

非线性Sturm—Liouville问题的一个三解定理

在利用上下解方法研究非线性微分方程多重解问题时，人们普遍使用基本条件－－非线性项满足单边Ｌｉｐｓｃｈｉｔｚ条件。本文在没有假定这个基本条件的情况下，利用上下解方法证明了非线性Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题的一个三解定理，从而改进了有关的已知结果。     

一类时滞反应扩散方程的周期解和概周期解

通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）解存在唯一性的充分条件．推广了已有的一些结果。     

Periodic Wave Solutions and Their Limits for the Modified Kd V–KP Equations

In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified Kd V–KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.     

关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

Qualitative analysis and explicit traveling wave solutions for the Davey–Stewartson equation

In this paper, we use the bifurcation method of dynamical systems to study the traveling wave solutions for the Davey–Stewartson equation. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic wave solutions, periodic blow‐up wave solutions, unbounded wave solutions, kink profile solitary wave solutions, and solitary wave solutions. Relations of the traveling wave solutions are given. Some previous results are extended. Copyright © 2013 John Wiley & Sons, Ltd.     

Some new nonlinear wave solutions and their convergence for the (2+1)‐dimensional Broer–Kau–Kupershmidt equation

We use the bifurcation method of dynamical systems to study the (2+1)‐dimensional Broer–Kau–Kupershmidt equation. We obtain some new nonlinear wave solutions, which contain solitary wave solutions, blow‐up wave solutions, periodic smooth wave solutions, periodic blow‐up wave solutions, and kink wave solutions. When the initial value vary, we also show the convergence of certain solutions, such as the solitary wave solutions converge to the kink wave solutions and the periodic blow‐up wave solutions converge to the solitary wave solutions. Copyright © 2014 John Wiley & Sons, Ltd.     

Solutions of the generalized Lennard-Jones system

In this paper, we study solution structures of the following generalized Lennard-Jones system in R~n,x=(-α/|x|~(α+2)+β/|x|~(β+2))x,with 0 α β. Considering periodic solutions with zero angular momentum, we prove that the corresponding problem degenerates to 1-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.     

Symbolic computation of exact solutions for a nonlinear evolution equation

In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here.     

Scalarization and optimality conditions for vector equilibrium problems

In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems.     

Several classes of exact solutions to the 1 + 1 Born–Infeld equation

We obtain closed-form exact solutions to the 1 + 1 Born–Infeld equation arising in nonlinear electrodynamics. In particular, we obtain general traveling wave solutions of one wave variable, solutions of two wave variables, similarity solutions, multiplicatively separable solutions, and additively separable solutions. Then, putting the Born–Infeld model into correspondence with the minimal surface equation using a Wick rotation, we are able to construct complex helicoid solutions, transformed catenoid solutions, and complex analogues of Scherk’s first and second surfaces. Some of the obtained solutions are new, whereas others are generalizations of solutions in the literature. These exact solutions demonstrate the fact that solutions to the Born–Infeld model can exhibit a variety of behaviors. Exploiting the integrability of the Born–Infeld equation, the solutions are constructed elegantly, without the need for complicated analytical algorithms.     

小展弦比波的Green-Naghdi渐进模型的行波解

本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解.     

Exact Solutions to Space-Time Fractional Fokas-Lenells Equations With Parameters北大核心CSCD

利用多项式完全判别系统法求得非线性光学中带参数时空分数阶Fokas-Lenells方程在一般情况下的精确解,包括有理函数解、周期解、孤波解、Jacobi椭圆函数解和双曲函数解等,绘制了精确解的相关图像,并由此分析了参数对解的结构的影响。