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本文研究具有外磁场的Landau-Lifshitz方程的全局动力学,具体包括局部适定性、全局适定性、周期解的存在性.首先,利用移动标架法将LandauLifshitz方程转化为半线性Schr?dinger方程,从而利用色散方程的技巧得到任意维的局部适定性和一维的全局适定性.其次,通过使用Landau-Lifshitz方程的对称性将周期解的存在性转化为常微分方程,从而证明了具有非零常值外磁场的Landau-Lifshitz方程具有非平凡的周期解,同时对于时间相关的外磁场,我们构造了若干具有典型动力学意义的特解. 相似文献
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mKdV方程的对称与群不变解 总被引:1,自引:0,他引:1
主要考虑mKdV方程的一些简单对称及其构成的李代数,并利用对称约化的方法将mKdV方程化为常微分方程,从而得到该方程的群不变解,这是对该方程群不变解的进一步扩展. 相似文献
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KdV-Burgers方程的对称与孤子解 总被引:1,自引:0,他引:1
考虑KdV-Burgers方程的一些简单对称及其构成的李代数,并利用对称约化方法将KdV-Burgers方程化为常微分方程,从而得到该方程的群不变解.此外,利用多项式展开式的方法去获得KdV-Burgers方程的新的孤子波解. 相似文献
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证明了当三维空间中各向异性Landau-Lifshitz方程的弱解满足稳定性条件时,其解具有部分正则性,并且对易面类型的方程,利用Ginzburg-Landau逼近构造了一个整体的部分正则解. 相似文献
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几类非线性差分方程的对称和精确解 总被引:1,自引:1,他引:0
本文将微分方程的Lie变换群方法推广到差分方程,给出了三类非线性差分方程的不变变换,利用这种变换由差分方程的平凡解得到非平凡的单参数解族。 相似文献
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运用李群对称方法解决Bretherton方程问题,得到方程的对称约化和群不变解,比如幂级数解,最后得出该问题的守恒率. 相似文献
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Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation 总被引:1,自引:0,他引:1
In this paper, symmetries and group invariant solutions to the Gardner-KP equation are obtained by using the direct symmetry method. At the same time, we find the corresponding Lie algebra, optimal system, classification and the similarity reductions to the equation, respectively. Our exact solutions generalize the corresponding results obtained by Wazwaz. In addition, the conservation laws of Gardner-KP equation are also given. 相似文献
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试图用李群方法来分析流体及渗流的运动规律.对于流形上流体、渗流力学方程的研究,物理空间的流动中的拓扑结构只要具有李群的性质,便可以此来进行流动分析.这是将李群理论直接、直地应用于渗流力学的一种方法.李群方法将众多求解特定类型的渗流微分方程方法统一到共同的概念之下.李群无穷小变换方法为寻找微分方程的闭合形式的解提供的广泛的应用,补充了求解渗流力学方程的数学物理技巧. 相似文献
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Based on the generalized symmetry group method presented by Lou and Ma [Lou and Ma, Non-Lie symmetry groups of (2 + 1)-dimensional nonlinear systems obtained from a simple direct method, J. Phys. A: Math. Gen. 38 (2005) L129], firstly, both the Lie point groups and the full symmetry group of the nonisospectral BKP equation are obtained, at the same time, a relationship is constructed between the new solutions and the old ones of equation. Secondly, the nonisospectral BKP can be proved to be Painlevé integrability by combining the standard WTC approach with the Kruskal’s simplification, some solutions are obtained by using the standard truncated Painlevé expansion. Finally, based on the relationship by the generalized symmetry group method and some solutions by using the standard truncated Painlevé expansion, some interesting solution are constructed. 相似文献
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Lie symmetry analysis, conservation laws and exact solutions of fourth-order time fractional Burgers equation 下载免费PDF全文
Chunyan Qin Shoufu Tian Li Zou Tiantian Zhang 《Journal of Applied Analysis & Computation》2018,8(6):1727-1746
In this paper, the fourth-order time fractional Burgers equation has been investigated, which can be used to describe gas dynamics and traffic flow. By employing the Lie group analysis method, the invariance properties of the equation are provided. With the aid of the sub-equation method, a new type of explicit solutions are well constructed with a detailed derivation. Furthermore, based on the power series theory, we investigate its approximate analytical solutions. Finally, its conservation laws with two kinds of independent variables are performed by making use of the nonlinear self-adjointness method. 相似文献
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Jian-gen Liu Xiao-Jun Yang Yi-Ying Feng Hong-Yi Zhang 《Journal of Applied Analysis & Computation》2020,10(3):1060-1072
Under investigation in this paper is a time fractional nonlinear diffusion equation which can be utilized to express various diffusion processes. The symmetry of this considered equation has been obtained via fractional Lie group approach with the sense of Riemann-Liouville (R-L) fractional derivative. Based on the symmetry, this equation can be changed into an ordinary differential equation of fractional order. Moreover, some new invariant solutions of this considered equation are found. Lastly, utilising the Noether theorem and the general form of Noether type theorem, the conservation laws are yielded to the time fractional nonlinear diffusion equation, respectively. Our discovery that there are no conservation laws under the general form of Noether type theorem case. This result tells us the symmetry of this equation is not variational symmetry of the considered functional. These rich results can give us more information to interpret this equation. 相似文献
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《Applied Mathematics Letters》2003,16(2):155-159
In this paper we give a group classification for a dissipation-modified Korteweg-de Vries equation by means of the Lie method of the infinitesimals. We prove that, by using the nonclassical method, we get several new solutions which are unobtainable by Lie classical symmetries. We obtain nonclassical symmetries that reduce the dissipation-modified Korteweg-de Vries equation to ordinary equations with the Painlevé property. These solutions have not been derived elsewhere by the singular manifold method. 相似文献