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1.
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.  相似文献   

2.
万晖* 《物理学报》2013,62(9):90203-090203
本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)ut=(g(x)D(u)ux)x+h(x)P(u)ux+q(x)Q(u)进行研究. 当扩散项D(u)取um (m≠-1,0,1)和eu两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解. 关键词: 广义条件对称 精确解 非线性反应扩散方程  相似文献   

3.
Lina Ji 《Physica A》2010,389(24):5655-5661
The second-order conditional Lie-Bäcklund symmetries of nonlinear diffusion equations with variable coefficients are studied. A number of examples are considered and some exact solutions are constructed via the compatibility of conditional Lie-Bäcklund symmetries and the governing equations. These solutions possess the extended forms of the separation of variables, including the extensions of the instantaneous source solutions of the porous medium equations.  相似文献   

4.
The functionally generalized variable separation solutions of a general KdV-type equations ut=uxxx + A(u, ux)uxx + B(u, ux) are investigated by developing the conditional Lie-Bäcklund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-Bäcklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.  相似文献   

5.
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.  相似文献   

6.
套格图桑  那仁满都拉 《物理学报》2011,60(9):90201-090201
本文为了获得非线性发展方程的无穷序列新精确解,进一步研究获得了第二种椭圆方程的几类新型解和Bäcklund变换.在此基础上,借助符号计算系统Mathematica,用带强迫项变系数组合KdV方程、(2+1)维和(3+1)维变系数Zakharov-Kuznetsov 方程为应用实例,构造了无穷序列新精确解.这里包括无穷序列Jacobi 椭圆函数光滑孤立子解、无穷序列Jacobi椭圆函数紧孤立子解、无穷序列三角函数紧孤立子解和无穷序列尖峰孤立子解. 关键词: 第二种椭圆方程 Bä cklund 变换 变系数非线性发展方程 无穷序列新精确解  相似文献   

7.
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples.  相似文献   

8.
李吉娜  朱晓宁  程利芳 《物理学报》2013,62(2):20201-020201
本文利用近似广义条件对称方法研究一类带有源项的非线性扩散方程的初值问题.给出所研究方程的分类并将偏微分方程的初值问题约化为常微分方程的初值问题,通过求解约化后的常微分方程组可得相对应偏微分方程初值问题的近似解.  相似文献   

9.
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples.  相似文献   

10.
张顺利  楼森岳  屈长征 《中国物理》2006,15(12):2765-2776
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt=Au,uxuxx+Bu,ux,ut which admits the derivative-dependent functional separable solutions DDFSSs). We also extend the concept of the DDFSS to cover other variable separation approaches.  相似文献   

11.
吉飞宇  张顺利 《物理学报》2012,61(8):80202-080202
讨论了带有扰动非线性源的多孔介质方程的近似泛函分离变量问题. 给出了该类方程容许近似泛函分离变量解的完全分类. 举例阐述了近似泛函分离变量解的求解步骤,获得了分类方程的近似泛函分离变量解.  相似文献   

12.
非线性Klein-Gordon方程新的精确解   总被引:1,自引:0,他引:1       下载免费PDF全文
韩兆秀 《物理学报》2005,54(4):1481-1484
将行波变换替换为更一般的函数变换,推广了修正的Jacobi椭圆函数展开方法.给出了非线性 Klein-Gordon方程新的周期解.当模m→1或m→0时,这些解退化成相应的孤立波解、三 角函数解和奇异的行波解.对于某些非线性方程,在一定条件下一般变换退化为行波约化. 关键词: Jacobi椭圆函数 非线性发展方程 精确解  相似文献   

13.
毛杰健  杨建荣 《物理学报》2007,56(9):5049-5053
用普通KdV方程作变换,构造变系数广义KdV方程的解,获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词: KdV方程 变系数广义KdV方程 类孤波解 精确解  相似文献   

14.
刘煜 《中国物理 B》2012,(11):41-46
The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed.  相似文献   

15.
This work is devoted to investigating exact solutions of generalized nonlinear fractional diffusion equations with external force and absorption. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solution, its diffusive behavior, and the sufficient and necessary conditions for solutions satisfying the boundary condition W(±∞,t)=0 and the sharp initial condition W(x,0)=δ(x).  相似文献   

16.
17.
姚若侠  李志斌 《中国物理》2002,11(9):864-868
Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions.  相似文献   

18.
套格图桑  伊丽娜 《物理学报》2014,63(16):160201-160201
首先给出一种函数变换,把一类非线性耦合系统化为两个第一种椭圆方程组.然后利用第一种椭圆方程的新解与B?cklund变换,构造了一类非线性耦合系统的无穷序列复合型双孤子新解.  相似文献   

19.
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples.  相似文献   

20.
套格图桑  那仁满都拉 《中国物理 B》2011,20(11):110203-110203
To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.  相似文献   

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