Klein-Gordon-Schrodinger方程组的精确孤立波解

利用齐次平衡原则导出Klein-Gordom-Schrodinger方程组的精确孤立波解.该解在形式上比文献中纯理论的存在性证明的结果更一般,文献中的解的形式是该结果的特殊情形.     

Klein-Gordon-Schrdinger方程组的精确孤立波解

利用齐次平衡原则导出Klein_Gordon_Schr dinger方程组的精确孤立波解·　该解在形式上比文献中纯理论的存在性证明的结果更一般 ,文献中的解的形式是该结果的特殊情形     

Klein—Gordon—Schrodinger方程组的精确弧立波解

利用齐次平衡原则导出Klein-Gordon-Schrodinger方程组的精确弧立波解。该解在形式上比献中纯理论的存在性证明的结果更一般，献中的解的形式是该结果的特殊情形。     

长水波近似方程组的新精确解

依据齐次平衡法的思想 ,首先提出了求非线性发展方程精确解的新思路 ,这种方法通过改变待定函数的次序 ,优势是使求解的复杂计算得到简化 .应用本文的思路 ,可得到某些非线性偏微分方程的新解 .其次我们给出了长水波近似方程组的一些新精确解 ,其中包括椭圆周期解 ,我们推广了有关长波近似方程的已有结果 .     

关于(2+1)-维色散的长波方程求解的一个注记

在文献[3]的基础上，根据一些简单方程的特征，导出了(2十1)—维色散的长波方程的新的精确解，其中包含了已有文献中的孤子解，多孤子解等．     

(2+1)维色散长波方程新的类孤子解

通过一个简单的变换,将(2+1)维色散长波方程简化为人们熟知的带强迫项Burgers方程,借助Mathematica软件,利用齐次平衡原则和变系数投影Riccati方程法,求出了(2+1)维色散长波方程新的精确解.     

（2＋1）维色散长波方程的扩展椭圆函数有理展开解法

在一个新的更一般的假设下,借助于符号计算,提出了一个椭圆函数有理展开法,并用它统一地求出许多非线性发展方程新的双周期精确解.本文选择(2+1)维色散长波方程作为此方法的应用来加以说明.得到了Yan方法所得的所有解,并且得到更多的一般形式的解.在m取它的极限时,可得到许多冲击波解和孤立波解.     

两个非线性发展方程精确解析解的研究

对齐次平衡法进行了改进并将其应用于两个非线性发展方程中,通过一些新的假设,获得了若干精确解析解,这些解包含王和张的结论及其它新类型的解析解,如果理分式解和周期解,这种方法也可以应用于求解更多的非线性偏微分方程。     

求二维DKdV方程精确解的方法

The exact soliton wave solution for the two-dimensional Korteweg-de Vires-Burgers equation is obtaind via introducing nonlinear transformations.This method,which is different from reference[1],here is very concise and primary.The metheod in this letter can be applied to other nonlinear equations.     

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．     

Exact solitary wave solutions of nonlinear wave equations

The hyperbolic function method for nonlinear wave equations is presented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Gr?bner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.     

Zhiber-Shabat方程的孤立波解与周期波解

结合齐次平衡法原理并利用F展开法,再次研究了Zhiber-Shabat方程的各种椭圆函数周期解.当椭圆函数的模m分别趋于1或0时,利用这些椭圆函数周期解,得到了Zhiber-Shabat方程的各种孤子解和三角函数周期解,从而丰富了相关文献中关于Zhiber-Shabat波方程的解的类型.     

Exact solitary wave solutions to a combined KdV and mKdV equation

An exact travelling wave kink soliton to a combination KdV and mKdV equations is given by using an effective homogeneous balance method, and a two‐dimensional generalization is also discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

广度kdv方程的精确解:改进的齐次平衡法

In this paper,we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method.Based on the modified homogeneous balance method,several kinds of exact(new)solutions of the generalized KdV equation are obtained.     

Exact solutions of Kolmogorov-Petrovskii-Piskunov equation using the modified simple equation method

The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov （KPP） equation. When certain parameters of the equations are chosen to be special values, the solitary wave solutions are derived from the exact solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.     

Exact traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation

Bifurcation method of dynamical systems is employed to investigate traveling wave solutions in the (2 + 1)-dimensional Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation. Under some parameter conditions, exact solitary wave solutions and kink wave solutions are obtained.     

Exact axially symmetric wave solutions of the Yang-Mills equations

We find a class of exact axially symmetric wave solutions of the Yang-Mills equations with SU(2) symmetry. The solutions in this class describe running waves propagating at the speed of light in a vacuum and contain two arbitrary differentiable functions of their phase. We consider properties of field sources that can generate such running waves. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 243–248, August, 2006.     

带有热源项的非线性扩散方程的精确解

讨论了带有热源项的非线性扩散方程.通过一种直接简洁的方法得到了几种精确解.该方法可用于更高阶演化方程的求解问题.     

Exact solutions of semilinear radial wave equations in n dimensions

Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system of group-invariant variables given by group foliations of the wave equation, using the one-dimensional admitted point symmetry groups. (These groups comprise scalings and time translations, admitted for any nonlinearity power, in addition to space-time inversions admitted for a particular conformal nonlinearity power.) This is shown to yield not only group-invariant solutions as derived by standard symmetry reduction, but also other exact solutions of a more general form. In particular, solutions with interesting analytical behavior connected with blow-ups as well as static monopoles are obtained.     

The extended hyperbolic functions method and new exact solutions to the Zakharov equations

The multiple exact solutions for the nonlinear evolution equations describing the interaction of laser–plasma are developed. The extended hyperbolic function method are employed to reveal these new solutions. The solutions include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the solitary wave solutions of a compound of the bell-type and the kink-type for n and E, the singular traveling wave solutions, periodic traveling wave solutions of triangle function types, and solitary wave solutions of rational function types. In addition to re-deriving all known solutions in a systematic way, several new and more general solutions can be obtained by using our method.