饱和非线性波导阵列的离散孤子

利用扩展的双曲函数展开法,对饱和离散非线性波导阵列模型离散非线性薛定谔方程进行了研究,获得了多组新的精确解析局域解,包括亮孤子解、暗孤子解,以及亮、暗复合孤子解等,并给出了这些解存在对方程系数的特殊约束关系.     

符号计算与非线性偏微分方程精确行波解

In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs.     

非线性Schroeginger方程的包络波形式新的精确解

采用一种双曲函数和一类新的辅助常微分方程相结合的方法给出非线性Schroeglnger方程的包络波形式的精确解．这种方法也可用于其他非线性发展方程的新的孤立波解．     

A Family of Exact Solutions fort the Nonlinear Schrodinger Equation

In this paper,the nonlinear Schrodinger(NLS)equation was analytically solved.Firstly,the stationary solutions of NLS equation were explicitly given by the elliptic functions.Then a family of exact solutions of NLS equation were botained from these stationary solutions by a method for finding new exact solutions from the stationary solutions of integrable evolution equations.     

离散非线性薛定谔方程的新孤子解

利用改进的双曲函数法,研究离散的非线性薛定谔方程,不仅得到了离散暗孤子解,还获得了离散亮孤子解以及其它一些新形式的离散类孤子解。这种方法也同样适用于求解其它离散的非线性波方程。     

离散的非线性Ablowitz方程的Jacobi椭圆函数解

基于Jacobi椭圆函数展开法求解离散的非线性Ablowitz方程,得到包含Jacobi椭圆正弦,Jacobi椭圆余弦,第三类Jacobi椭圆余弦的周期波解并表明在极限情形下得到孤立子解.     

河床流体模型方程的显式精确解

结合直接方法和假设方法得到了河床流体模型方程及其推广的一些显式精确行波解，这些解包括孤立波解、奇异行波解和三角函数状周期波解。     

Kupershmidt方程新的精确解析解

对齐次平衡法进行了改进，并将其应用于Kupershmidt方程中，通过假设一些新的形式解，获得了它的六类精确解析解。     

一类(2+1)维非线性波方程新解

使用Jacobi椭圆函数展开法 ,研究 (2 + 1)维KPI方程和 (2 + 1)维Bounessiq方程的周期解和孤波解 ,并借助计算机代数系统Maple ,通过图形分析法 ,给出多解     

某些孤子方程的新解

The novel multisoliton solutions for the nonlinear lumped self-dual network equations, Toda lattice and KP equation were obtained by using the Hirota direct method.     

辅助方程法求变系数Boussinesq方程的精确解

以辅助方程法为基础,结合函数变换,借助符号计算系统Mathematica构造变系数Boussinesq方程的新的类孤子解和三角函数波解。     

一类具有积分边界条件的非线性分数阶微分方程的正解

利用Guo/Krasnoselskii不动点定理研究一类具有积分边界条件的非线性分数阶微分方程边值问题正解的存在性。     

Klein-Gordon方程的精确解

主要利用直接截断法来讨论Klein-Gordon方程：utt-uxx＋αu-βu3=0的精确解.借助于符号计算软件Maple,得到了此方程一些新的含Jacobi椭圆函数的精确解.     

Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method

This paper applies the EXP-function method to find exact solutions of various nonlinear equations. Tzitzeica- Dodd-Bullough (TDB) equation was selected to illustrate the effectiveness and convenience of the suggested method. More generalized solitonary solutions with free parameters were obtained by suitable choice of the free parameters, and also the obtained solitonary solutions can be converted into periodic solutions.     

形变映射法求Boussinesq方程的显式精确行波解

利用形变映射法，建立Boussinesq方程与三次非线性Klein-Gordon(NKG)方程一类特殊类型解的代数变换关系．根据该关系以及NKG方程的已知解，获得Boussinesq方程系统丰富的显式精确行波解，包括孤波解，周期波解，雅可比椭圆函数解和其他精确解．     

非线性Sobolev-Galpern方程的整体强解

本文用连续延拓法（压缩映射原理结合解的一致先验估计）研究了非线性SobolevGalpem方程的初边值问题,得到了该问题整体强解的存在唯一性结果。     

高次非线性薛定谔微分方程的新精确解

主要利用直接截断法来讨论非线性薛定谔微分方程： iu1＋uxx＋α0｜u｜^2u＋i[γ1uxx＋γ2｜u｜^2ux＋γ3（｜u｜^2）xu]=0 的精确解．借助于符号计算软件Maple,得到了此方程一些新的含Jacobi椭圆函数的精确解。     

一类n维变系数非齐线性微分方程组特解的简捷求法

给出一类n维变系数非齐线性微分方程组特解的简捷求法 ,并提供了特解的表达式     

Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions

By using the upper and lower solutions method and fixed point theory, we investigate a class of fourth - order singular differential equations with the Sturm - Liouville Boundary conditions. Some sufficient conditions are obtained for the existence of C^2 [ 0, 1 ] positive solutions and C^3 [ 0, 1 ] positive solutions.     

Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions

By using the upper and lower solutions method and fixed point theory, we investigate a class of fourth - order singular differential equations with the Sturm - Liouville Boundary conditions. Some sufficient conditions are obtained for the existence of C2 [ 0, 1 ] positive solutions and C3 [ 0, 1 ] positive solutions.