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1.
对带有一般实参数第三类Painlevé方程,已有γ<0,δ>0时,解的有界性以及振荡渐近解的表达形式的结论.在本文中,我们给出当δ=0或γ=0时其振荡渐近解的表达形式. 相似文献
2.
The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has P... 相似文献
3.
A reaction diffusion system arising in the theory of superconductivity is considered and its many kinds of analytic solutions are constructed by the Painlev analysis and similarity reduction methods. 相似文献
4.
We use analytic methods to analyze the discrete spectrum for the problem (Z1eZ2)2 in the united-atom limit (R ≪ 1) and obtain asymptotic expansions for the quantum defect and energy terms of the system (Z1eZ2)2 at small intercenter distances R up to terms of the order O(R6). We investigate the effect of the dimensionality factor on the energy spectrum of the hydrogen molecular ion H
2
+
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 269–287, August, 2006. 相似文献
5.
In this paper,the Painlev’e properties of the modified C-KdV equation are verified by using the W-K algorithm.Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the nonstandard truncated expansion method with the help of Maple software,respectively. 相似文献
6.
In this paper,a variable-coefficient Benjamin-Bona-Mahony-Burger (BBMB) equation arising as a mathematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated.The integrability of such an equation is studied with Painlev analysis.The Lie symmetry method is performed for the BBMB equation and then similarity reductions and exact solutions are obtained based on the optimal system method.Furthermore different types of solitary,periodic and kink waves can be seen with the change of variable coefficients. 相似文献
7.
The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevé transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang’s symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows: (i) The first Painlevé ordinary differential equation, (ii) a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather “violent” phenomenon. 相似文献
8.
In this paper, we obtain a supersymmetric generalization for the
classical Boussinesq equation. We show that the supersymmetric
equation system passes the Painlev\'{e test and we also calculate
its one- and two-soliton solutions. 相似文献
9.
利用玻色化方法可以避免超对称可积系统中反对易费米场带来的计算困难. 本文以N=1超对称mKdVB系统为例, 利用玻色化方法, 将其转化为只有玻色场的耦合系统. 应用标准的WTC方法, 证明了该耦合系统具有Painlevé性质. 运用Painlevé截断方法, 可以得到玻色化后超对称mKdVB系统的非局域对称. 为了求解与非局域对称相关的Lie第一性原理, 引入新的场将玻色化后系统拓展为更大的系统. 通过引入新的场, 该非局域对称局域化为Lie点对称. 因此, 可以利用Lie点对称约化方法研究拓展后的系统, 得到超对称mKdVB系统的孤子与其他孤波相互作用解. 相似文献
10.
将Painlevé方法推广到更一般的形式, 可以从给定的低维可积模型中得到无穷多个新的可积模型. 新的可积模型与原模型相比都是较高维的, 它们保持保角不变性和Painlevé性质. 本文主要以KdV、NLS和KP方程为例, 运用WTC法、截断展开、领头项分析等方法, 给出了(3+1)维可积模型的具体形式. 相似文献