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1.
Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source 下载免费PDF全文
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
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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
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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
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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
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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
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ZHANG Shun-Li ZHU Xiao-Ning WANG Yong-Mao LOU Sen-Yue 《理论物理通讯》2008,49(4):829-832
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
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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
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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
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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
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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
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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
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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
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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
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ZHANG Shun-Li WANG Yong LOU Sen-Yue 《理论物理通讯》2007,47(6):975-980
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
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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