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Marcus Ansorg 《General Relativity and Gravitation》2001,33(2):309-338
In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Bäcklund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i.e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions. 相似文献
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辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bäcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解. 相似文献
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We prove that difference equations arising from consistent compositions of Bäcklund transformations of the continuous Painlevé equations possess the singularity confinement property. 相似文献
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Engui Fan 《Physics letters. A》2011,375(3):493-497
Binary Bell polynomials are extended to systematically construct bilinear formalism, bilinear Bäcklund transformations, Lax pairs and infinite conservation laws of the nonisospectral and variable-coefficient KdV equation in a quick and natural way. Moreover, the infinite conservation laws are local and obtained through directly decoupling binary Bell polynomials. 相似文献
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本文为了获得非线性发展方程的无穷序列新精确解,进一步研究获得了第二种椭圆方程的几类新型解和Bäcklund变换.在此基础上,借助符号计算系统Mathematica,用带强迫项变系数组合KdV方程、(2+1)维和(3+1)维变系数Zakharov-Kuznetsov 方程为应用实例,构造了无穷序列新精确解.这里包括无穷序列Jacobi 椭圆函数光滑孤立子解、无穷序列Jacobi椭圆函数紧孤立子解、无穷序列三角函数紧孤立子解和无穷序列尖峰孤立子解.
关键词:
第二种椭圆方程
Bä
cklund 变换
变系数非线性发展方程
无穷序列新精确解 相似文献
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To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations. 相似文献