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1.
累次齐次平衡法及其应用   总被引:1,自引:0,他引:1  
在求非线性偏微分方程精确解的过程中两次使用了齐次平衡法(称为累次齐次平衡法),解决了齐次平衡法求解少的不足,从而改进了齐次平衡法.以高阶(2+1)维Kadomtsev-Petviashvili方程和变异的Boussinesq方程为应用实例,说明使用累次齐次平衡法可以求得大量的精确解,其中许多解是新解或覆盖了其他方法所得的解.方法可应用于大量的非线性物理模型.  相似文献   

2.
长水波近似方程组的新精确解   总被引:3,自引:0,他引:3  
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 .  相似文献   

3.
本借助于计算机代数系统Mathematica.应用齐次平衡法.求出了具有效学物理意义的非线性BBM方程的准确解.若用该方法末解推广的B-BBM方程尚须进一步的研究.  相似文献   

4.
齐次平衡法是把非线性偏微分方程转换成带约束条件的线性偏微分方程的一种很好的方法 .本文在齐次平衡法的基础上具体讨论了KP方程的精确解 ,包括孤波解 ,一般的行波解 ,有理函数解和一种新类型的解 .  相似文献   

5.
齐次平衡方法的扩展及应用   总被引:19,自引:0,他引:19       下载免费PDF全文
该文对齐次平衡方法进行了扩展,并利用扩展所得的结果重新求出了一些非线性发展方程的精确解.  相似文献   

6.
两个非线性发展方程精确解析解的研究   总被引:6,自引:0,他引:6  
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。  相似文献   

7.
二维色散长波方程组的精确解   总被引:2,自引:0,他引:2  
利用齐次平衡法给出了二维色散长波方程组的定态解、孤立波解与非孤立波解等几种显式精确解。这个方法也可用来寻找其它非线性发展方程的不同类型的精确解。  相似文献   

8.
提出了寻求非线性发展方程行波解新的辅助方程法,作为实例通过选取变系数Bernoulli方程作为辅助常微分方程,并借助于计算机系统Mathematica和齐次平衡原则,求解了一类非线性发展方程,得到了该方程的新的显式精确解.所用方法可应用到其它类似方程的求解.  相似文献   

9.
求解非线性方程的双函数法   总被引:15,自引:0,他引:15  
基于齐次平衡法和李志斌的tanh函数法,得到简单有效的求解非线性发展方程的双函数法,这种方法利用非线性发展方程孤立波的局部性特点,把非线性方程的孤波解表示为函数f和g的多项式,并用这种方法求出了非线性波理论中的基本模型KdV方程的多组孤波解。  相似文献   

10.
应用齐次平衡法思想,求出非线性耗散项的Burgers-Fisher方程Bcklund变换、若干对称约化和相似解.  相似文献   

11.
By using the homogeneous balance method, we show that the dromion solutions exist for the (2+1)-dimensional dispersive long-wave equations. It is conjectured that the method used here can be generalized to a class of nonlinear evolution equation. The method here is very concise and primary.  相似文献   

12.
The repeated homogeneous balance is used to construct a new exact traveling wave solution of the Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can be applied to other nonlinear evolution equations.  相似文献   

13.
The extended homogeneous balance method is used to construct exact traveling wave solutions of a generalized Hirota–Satsuma coupled KdV equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many exact traveling wave solutions of a generalized Hirota–Satsuma coupled KdV equation are successfully obtained, which contain soliton-like and periodic-like solutions This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations.  相似文献   

14.
The extended homogeneous balance method with the aid of computer algebraic system Maple, is proposed for seeking the travelling wave solutions for a class of nonlinear evolution equations, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear evolution equations, respectively. Many new exact travelling wave solutions are successfully obtained. The method is straightforward and concise, and it can be also applied to other nonlinear evolution equations.  相似文献   

15.
The repeated homogeneous balance method is used to construct new exact traveling wave solutions of the (3 + 1) dimensional Kadomtsev–Petviashvili (KP) equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained, which contain soliton-like and periodic-like solutions. This method is straightforward and concise, and it can be also applied to other nonlinear evolution equations.  相似文献   

16.
Based on the homogeneous balance method,the Jacobi elliptic expansion method and the auxiliary equation method,the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations.New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple.The method is also valid for other (1+1)-dimensional and higher dimensional systems.  相似文献   

17.
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.  相似文献   

18.
高阶(2+1)维Broer-Kaup方程的局域相干结构   总被引:1,自引:0,他引:1  
利用推广的齐次平衡方法,研究高阶(2+1)维Broer-Kaup方程的局域相干结构。首先基于推广的齐次平衡方法,给出了这个模型的一个非线性变换,并把它变换成一个线性化的方程。然后从线性化方程出发,2构造出一个分离变量的拟解。由于拟解中不仅含有两个y的任意函数,而且还有{αu,βi,γi,kj,lk}和{N,M,L}这些参数可以任意选取,因此合适的选择这些函数和参数,可以得到新的相当丰富的孤子结构。方法直接而简单,可推广应用一大类(2+1)维非线性物理模。  相似文献   

19.
A nonlinear transformation for the cylindrical KP(CKP) equation has been derived by using the simplified homogeneous balance method (SHB). The 1-decay mode and 2-decay mode solutions of the CKP equation have been obtained in terms of the nonlinear transformation derived here. The results obtained in the paper are different from those reported earlier.  相似文献   

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