一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

Urysohn方程数值解的一个高精度算法

Kumar和Sloan[1]及Atkinson,Flores[3]将配置法用于Hammerstein方程，并证明了在适当条件下近似解的迭代是超收敛的．这里针对于一般的vrysotri方程给出了一个近似解的迭代校正计算格式，证明了近似解不论是用什么方法求得的，在适当条件下迭代校正算法总具有超收敛性．将（1）     

用Riccati方程的新解求Fitzhugh-Nagumo方程的新行波解

本文研究了Riccati方程和Fitzhugh-Nagumo方程的新精确解的构造.利用试探函数法找到了Riccati方程的八种类型的新显式精确解.用广义Tanh函数法结合Riccati方程的新精确解,获得了Fitzhugh-Nagumo方程、Huxley方程、广义KPP方程及Newell-Whitehead方程的许多新...     

一般非线性Schrödinger方程的显式孤立波解

本文考虑推广的导数非线性Schrodinger方程;运用动力系统的几何理论、分支理论和直接方法,得到其指定形式的所有显式精确孤立波解.本文的结果包含和推广了关于这一方程的显式精确孤立波解的所有已知结果.     

一般非线性Schr(o)dinger方程的显式孤立波解

本文考虑推广的导数非线性Schrodinger方程;运用动力系统的几何理论、分支理论和直接方法,得到其指定形式的所有显式精确孤立波解.本文的结果包含和推广了关于这一方程的显式精确孤立波解的所有已知结果.     

一般非线性Schrdinger方程的显式孤立波解

本文考虑推广的导数非线性 Schrodinger 方程;运用动力系统的几何理论、分支理论和直接方法,得到其指定形式的所有显式精确孤立波解。本文的结果包含和推广了关于这一方程的显式精确孤立波解的所有已知结果。     

■－方程的积分解算子的局部C~k－边界正则性

作为ＣｈｅｎＺ．［１］的推广，文中证明了（ｐ，ｑ）－形式的三方程的Ｋｏｐｐｅｌｍａｎ－Ｌｅｒａｙ算子Ｔｐ，ｑ和Ｋｏｐｐｅｌｍａｎ算子Ｈｐ，ｑ解在具片段Ｃ１－边界的开集Ｄ上局部地保持边界点的实解析性．     

一般非线性Schroedinger方程的显式孤立波解

本文考虑推广的导数非线性Schroedinger方程；运用动力系统的几何理论、分支理论和直接方法，得到其指定形式的所有显式精确孤立波解．本文的结果包含和推广了关于这一方程的显式精确孤立波解的所有已知结果．     

几个非线性发展方程的精确解

应用改进F/G展开法求得(2+1)维BBM方程、(1+1)维Benjiamin Ono方程、广义(2+1)维ZK-MEW方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明,F/G展开法在非线性发展方程中具有广泛的应用.     

一个包含k次补数的方程

研究一个包含k次补数的方程问题,利用初等方法,给出一个包含k次补数方程的所有解,证明这一方程的所有解.     

KK方程和改进的Boussinesq方程的新精确解

应用改进的Fan's代数方法,得到了KK方程和改进的Boussinesq方程的一系列新精确解,包括孤立波解、类孤立波解、纽结波解、奇异纽结波解和三角函数周期解.     

浅水波方程和Klein-Gordon方程新的精确行波解

采用了一种新的方法来求解浅水波方程和Klein-Gordon的行波解.在该方法下,Klein-Gordon方程和浅水波方程都得到了其精确的周期孤立波解,从而该方法的有效性得到了验证.     

Peakon and cuspon solutions of a generalized Camassa-Holm-Novikov equation

The bounded traveling wave solutions of a generalized Camassa-Holm-Novikov equation with $p=2$ and $p=3$ are derived via the dynamical system approach. The singular wave solutions including peakons and cuspons are obtained by the bifurcation analysis of the corresponding singular dynamical system and the orbits intersecting with or approaching the singular lines. The results show that the generalized Camassa-Holm-Novikov equation with $p=2$ and $p=3$ both admit smooth solitary wave, smooth periodic wave solutions, solitary peakons, periodic peakons, solitary cuspons and periodic cuspons as well. It is worth pointing out that the Novikov equation has no bounded traveling wave solutions with negative wave speed, but has a family of new periodic cuspons which are distinguished with the normal periodic cuspons for their discontinuous first-order derivatives at both maximum and minimum.     

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.     

应用指数函数展开法求解非线性发展方程

利用指数函数展开法,研究BBM方程与KG方程,在一个特定的变换下,借助Maple软件的符号运算功能,获得BBM方程与KG方程指数函数型新的孤立波解与周期解.这种方法用于求解非线性发展方程是简单而有效的.     

New explicit solutions for the Klein-Gordon equation with cubic nonlinearity

In this paper, we investigate Klein-Gordon equation with cubic nonlinearity. All explicit expressions of the bounded travelling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded travelling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.     

广义Riccati展开法及其在foam drainage方程中的应用

应用双曲函数法结合Riccati方程,求得foam drainage方程的精确解.通过这种方法可以得到此方程的新的孤立波解与周期解,并且此方法可以用来求解其它许多的非线性演化方程.     

利用F-展开法求解ZK-BBM方程

利用F-展开法求解出了ZK-BBM方程的双周期波解,并在极限形式下得到了ZK-BBM方程的孤波解和单周期波解.从而丰富了该方程解的理论.此方法也可适用求解其它非线性发展方程.     

New travelling wave solutions for a nonlinearly dispersive wave equation of Camassa-Holm equation type

In this paper, the integral bifurcation method is used to study a nonlinearly dispersive wave equation of Camassa-Holm equation type. Loop soliton solution and periodic loop soliton solution, solitary wave solution and solitary cusp wave solution, smooth periodic wave solution and non-smooth periodic wave solution of this equation are obtained, their dynamic characters are discussed. Some solutions have an interesting phenomenon that one solution admits multi-waves when parameters vary.     

广义组合KdV-mKdV方程的显式精确解

Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations.