scholarly journals Solutions of the spherically symmetric wave equation in p+q dimensions

1995 ◽  
Vol 36 (1) ◽  
pp. 383-397
Author(s):  
W. Bietenholz ◽  
J. J. Giambiagi
Keyword(s):  
Wave Equation ◽  
Spherically Symmetric ◽  
Symmetric Wave

Numerical Determination of Pseudobreathers of a Three-Dimensional Spherically Symmetric Wave Equation

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Janusz Karkowski
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Numerical Determination ◽  
Pseudospectral Methods ◽  
Symmetric Wave ◽  
Long Time ◽  
Signum Function ◽  
Continuous Approximations

A numerical method for finding spherically symmetric pseudobreathers of a nonlinear wave equation is presented. The algorithm, based on pseudospectral methods, is applied to find quasi-periodic solutions with force terms being continuous approximations of the signum function. The obtained pseudobreathers slowly radiate energy and decay after some (usually long) time depending on the period that characterizes (unambiguously) the initial configuration.

The fundamental solution for the axially symmetric wave equation II

1980 ◽  
Vol 87 (3) ◽  
pp. 515-521
Author(s):  
Albert E. Heins
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Fundamental Solution ◽  
Free Space ◽  
Axially Symmetric ◽  
Partial Differential ◽  
Symmetric Wave ◽  
Alternate Forms ◽  
Image Position

In a recent paper, hereafter referred to as I (1) we derived two alternate forms for the fundamental solution of the axially symmetric wave equation. We demonstrated that for α > 0, the fundamental solution (the so-called free space Green's function) of the partial differential equationcould be written asif b > rorif r > b.

scholarly journals Wave equation on spherically symmetric Lorentzian metrics

2011 ◽  
Vol 52 (6) ◽  
pp. 063511 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Ahmad Y. Al-Dweik ◽  
A. H. Kara ◽  
M. Karim ◽  
F. D. Zaman
Keyword(s):  
Wave Equation ◽  
Spherically Symmetric ◽  
Lorentzian Metrics

Isospectral sets for transmission eigenvalue problem

2020 ◽  
Vol 28 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Sergey A. Buterin
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Wave Speed ◽  
Spherically Symmetric ◽  
Variable Speed ◽  
Transmission Eigenvalues ◽  
Constructive Methods ◽  
Transmission Eigenvalue ◽  
Symmetric Variable ◽  
Transmission Eigenvalue Problem

AbstractWe consider the boundary value problem {R(a,q)}: {-y^{\prime\prime}(x)+q(x)y(x)=\lambda y(x)} with {y(0)=0} and {y(1)\cos(a\sqrt{\lambda})=y^{\prime}(1)\frac{\sin(a\sqrt{\lambda})}{\sqrt{% \lambda}}}. Motivated by the previous work [T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems 29 2013, 6, Article ID 065007], it is natural to consider the following interesting question: how does one characterize isospectral sets corresponding to problem {R(1,q)}? In this paper applying constructive methods we answer the above question.

scholarly journals GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL DEFOCUSING NONLINEAR WAVE EQUATION FOR SPHERICALLY SYMMETRIC DATA

2007 ◽  
Vol 04 (02) ◽  
pp. 259-265 ◽  
Author(s):  
TERENCE TAO
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Regularity ◽  
Spherically Symmetric ◽  
Supercritical Regime ◽  
Critical Equation ◽  
Critical Regularity ◽  
Spatial Dimensions ◽  
Symmetric Initial Data ◽  
Supercritical Wave Equation

We establish global regularity for the logarithmically energy-supercritical wave equation □u = u5 log (2 + u2) in three spatial dimensions for spherically symmetric initial data, by modifying an argument of Ginibre, Soffer and Velo for the energy-critical equation. This example demonstrates that critical regularity arguments can penetrate very slightly into the supercritical regime.

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