共查询到18条相似文献,搜索用时 578 毫秒
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为了获得非线性差分微分方程的无穷序列精确解,引入一种双曲函数型辅助方程,并给出该方程解的Bcklund变换和解的非线性叠加公式.在此基础上,利用辅助方程与函数变换相结合的方法,借助符号计算系统Mathematica,用一般格子方程为应用实例,获得了无穷序列精确解。 相似文献
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溃坝洪水长波与地面障碍物作用的数值模拟 总被引:2,自引:0,他引:2
利用TVD差分格式设计思想,给出了一种数值求解浅水波方程的数值方法,经过数值解与精确解的比较,表明该方法很好地模拟溃坝洪水洪间断面的位置和形状。进一步对溃坝洪水水波与地面障碍物的作用进行数值模拟,得到了合理的结果。 相似文献
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Generalized conditional symmetry method for tackling nonlinear partial differential equations is extended to differential-difference equations. As the applications, some exact solutions to several nonlinear differential-difference equations are obtained. 相似文献
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An improved algorithm is devised for using the (G′/G)-expansion method to solve nonlinear differential-difference equations. With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with parameters are obtained, from which some special solutions including the known solitary wave solution are derived by setting the parameters as appropriate values. It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics. 相似文献
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LIU Shi-Kuo FU Zun-Tao WANG Zhang-Gui LIU Shi-Da 《理论物理通讯》2008,49(5):1155-1158
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained. 相似文献
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In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation. 相似文献
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In this work, an adaptation of the
tanh/tan-method that is discussed usually in the nonlinear partial
differential equations is presented to solve nonlinear polynomial
differential-difference equations. As a concrete example, several
solitary wave and periodic wave solutions for the chain
which is related to the relativistic Toda lattice are derived.
Some systems of the differential-difference equations that can be solved using our approach
are listed and a discussion is given in conclusion. 相似文献
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XIE Fu-Ding 《理论物理通讯》2005,44(8)
Some soliton solutions and periodic solutions of hybrid lattice, discretized mKdV lattice, and modified Volterra lattice have been obtained by introducing a new method. This approach allows us to directly construct some explicit exact solutions for polynomial nonlinear differential-difference equations. 相似文献
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A Hierarchy of Differential-Difference Equations and Their Integrable Couplings 总被引:1,自引:0,他引:1 下载免费PDF全文
Starting from a discrete spectral problem, the corresponding hierarchy of nonlinear differential-difference equation is proposed. It is shown that the hierarchy possesses the bi-Hamiltionian structures. Further, two integrable coupling systems for the hierarchy are constructed through enlarged Lax pair method. 相似文献
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《Physica A》2007
We describe in elementary terms how eigenmode expansions can be used to deal with differential-difference equations. As particular applications we present the full analytical solution of linear stochastic time-delay systems and the weakly nonlinear analysis of nonlinear differential-difference equations in the limit of large time delay. Our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the Lambert W-function and on the explicit formula for the eigenfunctions of the adjoint equation. 相似文献