Construction of metric and vector potential perturbations of a Reissner–Nordström black hole

1979 ◽  
Vol 369 (1736) ◽  
pp. 67-81 ◽  
Keyword(s):  
Black Hole ◽  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Explicit Formulae

When an appropriate decoupling of variables in a coupled linear system of partial differential equations is obtained, a recently described procedure enables one to construct solutions to the full coupled system of equations. We employ this procedure here to generate solutions of the linearized Einstein–Maxwell equations describing perturbations of a Reissner–Nordström black hole, using Chandrasekhar’s recent decoupling of these equations. Explicit formulae are given for the metric and vector potential perturbations for each parity type.

scholarly journals An uncoupling procedure for a class of coupled linear partial differential equations

1985 ◽  
Vol 26 (4) ◽  
pp. 503-516 ◽  
Author(s):  
A. McNabb
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Large Class ◽  
Partial Differential Operator ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Similar System ◽  
Linear Partial Differential Equations

AbstractA Fredholm operator exists which maps the solutions of a system of linear partial differential equations of the form ∂u/∂t = DLu + Au coupled by a matrix A onto those solutions of a similar system coupled by a matrix B which have the same initial values. The kernels of this operator satisfy a hyperbolic system of equations. Since these equations are independent of the linear partial differential operator L, the same operator serves as a mapping for a large class of equations. If B is chosen diagonal, the solutions of a coupled system with matrix A may be obtained from the uncoupled system with matrix B.

scholarly journals Topology and factorization of polynomials

2009 ◽  
Vol 104 (1) ◽  
pp. 51 ◽  
Author(s):  
Hani Shaker
Keyword(s):  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Vector Space ◽  
System Of Equations ◽  
Partial Differential ◽  
Linear System Of Equations ◽  
Complete Factorization ◽  
Factorization Of Polynomials

For any polynomial $P\in {\mathsf C} [X_1,X_2,\ldots,X_n]$, we describe a $\mathsf C$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

scholarly journals On the influence of the initial data in a combustion problem

1980 ◽  
Vol 22 (2) ◽  
pp. 193-209 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Temporal Evolution ◽  
Initial Conditions ◽  
Coupled System ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Approximate Expressions ◽  
Combustion Problem

AbstractThe combustion of a material can be modelled by two coupled parabolic partial differential equations for the temperature and concentration of the material. This paper deals with properties of the solution of these equations inside a cylinder or a sphere and under given initial conditions. Bounds for the variation of the temperature with the initial conditions are first established by considering a decoupled form of the equations. Then the coupled system is used to obtain approximate expressions for the temporal evolution of temperature and concentration.

scholarly journals Extension of Optimal Homotopy Asymptotic Method with Use of Daftardar–Jeffery Polynomials to Coupled Nonlinear-Korteweg-De-Vries System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Rashid Nawaz ◽  
Zawar Hussain ◽  
Abraiz Khattak ◽  
Adam Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Asymptotic Method ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Higher Order ◽  
Partial Differential ◽  
De Vries ◽  
Optimal Homotopy Asymptotic Method

In this paper, Daftardar–Jeffery Polynomials are introduced in the Optimal Homotopy Asymptotic Method for solution of a coupled system of nonlinear partial differential equations. The coupled nonlinear KdV system is taken as test example. The results obtained by the proposed method are compared with the multistage Optimal Homotopy Asymptotic Method. The results show the efficiency and consistency of the proposed method over the Optimal Homotopy Asymptotic Method. In addition, accuracy of the proposed method can be improved by taking higher order approximations.

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