共查询到16条相似文献,搜索用时 125 毫秒
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《物理学报》2009,58(11)
将(G'/G)展开首次法扩展到构造高维非线性物理方程的精确非行波通解、研究解的特殊孤子结构和混沌行为.作为(G'/G)展开法的新应用,获到了(3+1)维非线性Burgers系统的新非行波通解,对通解中的任意函数进行适当的设置,探讨了特殊孤子结构的激发和演化、解的混沌行为和演化.Abstract: The (G'/G)-expansion method is firstly extended to construct exact non-traveling wave general solutions of high-dimensional nonlinear equations, explore special soliton-structure excitation and evolution, and investigate the chaotic patterns and evolution of these solutions. Taking as an example, new non-traveling solutions are calculated for (3 + 1)-dimensional nonlinear Burgers system by using the (G'/G)-expansion method. By setting properly the arbitrary function in the solutions, special soliton-structure excitation and evolution are observed, and the chaotic patterns and evolution are studied for the solutions. 相似文献
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对(G′/G)展开法做了进一步的研究,利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题.借助Riccati方程的B?cklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解.这样,利用(G′/G)展开法可以获得非线性发展方程的无穷序列解,这一方法是对已有方法的扩展,与已有方法相比可获得更丰富的无穷序列解.以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解.这一方法可以用来构造其他非线性发展方程的无穷序列解. 相似文献
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对(G’/G)展开法进行了扩展, 引入了新的辅助方程, 对(G’/G)展开式附加了负指数幂, 并利用扩展的(G’/G)展开法求出了Zakharov方程组的一些新精确解. 该方法还可被应用到其他非线性演化方程中去.
关键词:
G’/G)展开法')" href="#">(G’/G)展开法
Zakharov方程组
精确解 相似文献
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提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统. 相似文献
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本文为了获得非线性发展方程新的无穷序列精确解,给出了几种辅助方程的Böcklund变换和解的非线性叠加公式,并构造了一些非线性发展方程新的无穷序列精确解,其中包括无穷序列Jacobi椭圆函数解、无穷序列双曲函数解和无穷序列三角函数解.该方法在构造非线性发展方程无穷序列精确解方面具有普遍意义.
关键词:
辅助方程法
解的非线性叠加公式
无穷序列解
非线性发展方程 相似文献
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A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation 下载免费PDF全文
Recently the (G'/G)-expansion
method was proposed to find the traveling wave solutions of
nonlinear evolution equations. This paper shows that the
(G'/G)-expansion method is a special form of the truncated
Painlevé expansion method by introducing an intermediate
expansion method. Then the generalized
(G'/G)--(G'/G) expansion method is naturally
derived from the standpoint of the nonstandard truncated
Painlevé expansion. The application of the generalized method to
the mKdV equation shows that it extends the range of exact solutions
obtained by using the (G'/G)-expansion
method. 相似文献
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In this article, we propose an alternative approach of the generalized and improved (G'/G)-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations. 相似文献
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This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method. 相似文献
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In this paper, we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation by using the (G'/G)-expansion method, and with the help of Maple. As a result, non-travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. This method can beapplied to other higher-dimensional nonlinear partial differential equations. 相似文献
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In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established. 相似文献
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This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the (ω/g)-expansion method, which can be thought of as the generalization of (G /G)-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained. 相似文献