共查询到20条相似文献,搜索用时 109 毫秒
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得到了双曲Yamabe流的一些精确解.第一类解是具有初始度量为Einstein的解,第二类解是具有轴对称的解.最后,作为这种流的特殊解,定义了稳定双曲Yamabe孤子,而且得到了这种孤子解所满足的方程. 相似文献
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基于Einstein方程和Hamilton Ricci流为背景,孔德兴和刘克峰最近提出了耗散双曲几何流的概念.考虑耗散双曲几何流Cauchy问题,证明了对于任意给定的初始度量,总存在初始的对称张量,使得经典解整体存在,并且对应的曲率保持一致有界.否则,其经典解会在有限时间内破裂. 相似文献
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杨征 《应用数学与计算数学学报》2013,(4):415-420
利用Riccati方程映射法和变量分离法,得到了推广的(2+1)维浅水波系统的变量分离解(包括孤波解、周期波解和有理函数解).根据得到的孤波解,构造出了方程的单孤子和双孤子结构,研究了孤子的混沌行为. 相似文献
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利用Hirota双线性方法求解了一个非等谱广义耦合非线性Schr(o|¨)dinger方程,得到它的N-孤子解.其中单孤子可以描述一个任意大振幅且具有时间和空间双重局部性的孤立波,这种特征与所谓的"怪波"相一致.此外,借助于图像描述了二孤子的相互作用. 相似文献
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利用同伦映射方法研究了一类非线性广义强迫扰动Klein-Gordon方程.首先利用双曲正切待定系数法求得了无扰动项典型方程的孤子解.然后利用同伦映射原理得到了强迫扰动Klein-Gordon方程的任意次近似孤子解.最后叙述了得到的近似孤子解是一个解析展开式,还能对它进行解析运算.这对使用简单的模拟方法得到的近似解是达不到的. 相似文献
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在Mathematica符号计算软件的帮助下,利用拓展的G'/G展开法和变量分离法,得到(2+1)维耗散长波方程的新精确解,通过选取合适的函数,可以构造出dromion解、Solitoff解、周期孤波解等,并进一步研究孤子随时间的演化过程. 相似文献
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《数学物理学报(A辑)》2016,(2)
该文从新谱问题出发,得到一个新的(2+1)-维广义Broer-Kaup-Kupershmidt孤子方程在Lax对非线性化下被分解成可积的常微分方程.接着,给出了一个有限维Hamilton系统并且证明在Liouville意义下是完全可积的.通过引进Abel-Jacobi坐标把Hamilton流进行了拉直,借助Riemannθ函数得到了(2+1)-维Broer-Kaup-Kupershmidt孤子方程的拟周期解. 相似文献
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Qi S. Zhang 《Geometriae Dedicata》2003,101(1):153-165
We prove the existence of positive, finite energy solutions to the Yamabe equation
on some noncompact manifolds with positive scalar curvature. We also clarify a published result on the existence of 'complete solutions' on those manifolds. 相似文献
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Samy Skander Bahoura 《Journal of Functional Analysis》2007,242(2):550-562
We give some a priori estimates for Yamabe equation on Riemannian manifold in dimensions 5 and 6. In dimension 5 we present an inequality of type sup×inf. In dimension 6, we have an estimate if we assume that the infima of the solutions are uniformly bounded below by some positive constant. 相似文献
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For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds. 相似文献
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ZHANG YongBing 《中国科学A辑(英文版)》2009,(8)
We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds. 相似文献
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In this paper we investigate the problem of existence of solutions for a super-critical fourth order Yamabe type equation and we exhibit a family of solutions concentrating at two points, provided the domain contains one hole and we give a multiplicity result if we are given multiple holes. 相似文献
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Fanqi Zeng 《数学研究》2021,54(4):371-386
We introduce the concept $h$-almost Yamabe soliton which extends naturally
the almost Yamabe soliton by Barbosa-Ribeiro and obtain some rigidity results concerning $h$-almost Yamabe solitons. Some condition for a compact $h$-almost Yamabe
soliton to be a gradient soliton is also obtained. Finally, we give some characterizations for a special class of gradient $h$-almost Yamabe solitons. 相似文献
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Habib Ammari 《Journal of Mathematical Analysis and Applications》2003,286(1):51-63
We consider the model that has been suggested by Greenberg et al. (Physica D 134 (1999) 362-383) for the ferroelectric behavior of materials. In this model, the usual (linear) Maxwell's equations are supplemented with a constitutive relation in which the electric displacement equals a constant times the electric field plus an internal polarization variable which evolves according to an internal set of nonlinear Maxwell's equations. For such model we provide rigorous proofs of global existence, uniqueness, and regularity of solutions. We also provide some preliminary results on the long-time behavior of solutions. The main difficulties in this study are due to the loss of compactness in the system of Maxwell's equations. These results generalize those of Greenberg et al., where only solutions with TM (transverse magnetic) symmetry were considered. 相似文献
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Lszl Simon 《Mathematische Nachrichten》2000,217(1):175-186
In this paper, existence of weak solutions of second order evolution equations is proved and some properties of the solutions are shown. The results are applied to higher order nonlinear hyperbolic functional differential equations. 相似文献
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Motivated by the definition of combinatorial scalar curvature given by Cooper and Rivin, we introduce a new combinatorial scalar curvature. Then we define the discrete quasi-Einstein metric, which is a combinatorial analogue of the constant scalar curvature metric in smooth case. We find that discrete quasi-Einstein metric is critical point of both the combinatorial Yamabe functional and the quadratic energy functional we defined on triangulated 3-manifolds. We introduce combinatorial curvature flows, including a new type of combinatorial Yamabe flow, to study the discrete quasi-Einstein metrics and prove that the flows produce solutions converging to discrete quasi-Einstein metrics if the initial normalized quadratic energy is small enough. As a corollary, we prove that nonsingular solution of the combinatorial Yamabe flow with nonpositive initial curvatures converges to discrete quasi-Einstein metric. The proof relies on a careful analysis of the discrete dual-Laplacian, which we interpret as the Jacobian matrix of curvature map. 相似文献
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Thierry Aubin 《Journal of Functional Analysis》2006,240(1):269-289
In this article we prove, among other things, some results about two problems which are the subject of announces these last decades: (1) the compactness of the set of the solutions of the Yamabe equation on a compact Riemannian manifold, (2) a generalization of a result of the author which is necessary to solve the Yamabe problem, when 2ω?n−6. 相似文献