A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On Classification of Symmetry Reductions for the Eikonal Equation

2016
*
Symmetry
*

We study

doi:10.3390/sym8060051
fatcat:phhnocsmhne2xhhzan26oee7nq
*the*relationship between*the*classification*of*three-dimensional nonconjugate subalgebras*of**the*Lie algebra*of**the*Poincaré group P(1, 4) and*the*types*of**symmetry*reduction*of**the**eikonal**equation*... to ordinary differential*equations*(ODEs). ... Conflicts*of*Interest:*The*authors declare no conflict*of*interest. ...##
###
Symmetry Reduction and Exact Solutions of the Eikonal Equation

1996
*
Journal of Nonlinear Mathematical Physics
*

*The*corresponding

*symmetry*reduction has been done. By means

*of*

*the*solutions

*of*

*the*reduced

*equations*some classes

*of*exact solutions

*of*

*the*investigated

*equation*have been presented. ... By means

*of*splitting subgroups

*of*

*the*generalized Poincaré group P(1, 4), ansatzes which reduce

*the*

*eikonal*

*equation*to differential

*equations*with fewer independent variables have been constructed. ...

*The*corresponding

*symmetry*reduction has been done. Using

*the*solutions

*of*

*the*reduced

*equations*, we have found some classes

*of*exact solutions

*of*

*the*

*eikonal*

*equation*. 1. ...

##
###
The symmetry and some exact solutions of the relativistic eikonal equation

1982
*
Lettere al Nuovo Cimento
*

We discuss

doi:10.1007/bf02754808
fatcat:bxoe22bcp5ay5eex5mnt33aype
*the**symmetry*group*of**the*relativistic*eikonal**equation*. It is found to be*the*conformal group C1,4*of**the*(4 + 1)-dimensional Poincaré-Minkowski space. ... Some exact multiparametrical solutions*of**the**equation*are obtained. ... Remarks Firstly, it id important to note that what has been said about*the**symmetry**of*eq. (2) holds true for*the**equation*Secondly,*the**symmetry*group*of*eq. (1) with m = 0 turns out to be an infinitedimensional ...##
###
On Integration of the Nonlinear d'Alembert-Eikonal System and Conditional Symmetry of Nonlinear Wave Equations

1997
*
Journal of Nonlinear Mathematical Physics
*

We study integrability

doi:10.2991/jnmp.1997.4.1-2.6
fatcat:rzuvuynqwrgkxclnjimntpj2g4
*of*a system*of*nonlinear partial differential*equations*consisting*of**the*nonlinear d'Alembert*equation*2u = F (u) and nonlinear*eikonal**equation*u xµ u x µ = G(u) in*the*complex ... Solutions found in this way are shown to correspond to conditional*symmetry**of**the**equations*enumerated above. ... Saying about*the*d'Alembert-*eikonal*system, we mean*the*system*of*two nonlinear partial differential*equations*(PDEs) which consists*of**the*nonlinear d'Alembert and*eikonal**equations*taken together 2u ...##
###
Symmetries of generalized soliton models and submodels on target spaceS2

2005
*
Journal of High Energy Physics
*

Here we calculate all

doi:10.1088/1126-6708/2005/01/004
fatcat:jtzpcwowzzccdnn6krrn4fyuou
*the**symmetries**of*these models and their submodels by*the*prolongation method. ... Some physically relevant non-linear models with solitons, which have target space S^2, are known to have submodels with infinitly many conservation laws defined by*the**eikonal**equation*. ... Further, CA acknowledges support from*the*Austrian START award project FWF-Y-137-TEC and from*the*FWF project P161 05 NO 5*of*N.J. Mauser. ...##
###
Traveltime approximations for transversely isotropic media with an inhomogeneous background

2011
*
Geophysics
*

Using perturbation theory and Taylor's series, I expand

doi:10.1190/1.3555040
fatcat:4tzize3m7zcezl3uayl4hpxdme
*the*solutions*of**the**eikonal**equation*for 2D transversely isotropic media with respect to*the*independent parameter θ,*the*angle*the*tilt*of**the*... axis*of**symmetry*makes with*the*vertical, in a generally inhomogeneous TI background with a vertical axis*of**symmetry*(VTI). ...*of*traveltime, into*the**eikonal**equation*3. ...##
###
Solutions of the Helmholtz equation given by solutions of the eikonal equation
[article]

2017
*
arXiv
*
pre-print

We find

arXiv:1706.04120v1
fatcat:5dk44wq6dna7jdno4s6ikpc5e4
*the*form*of**the*refractive index such that a solution, S,*of**the**eikonal**equation*yields an exact solution, ( i k_0 S),*of**the*corresponding Helmholtz*equation*. ... Acknowledgements One*of**the*authors (I R-G) thanks PRODEP-SEP for financial support through a postdoctoral scholarship DSA/103.5/16/5800 and also*the*Sistema Nacional de Investigadores (México). ... [1] , there exists a similar relation between solutions*of**the*Helmholtz*equation*and solutions*of**the**eikonal**equation*. ...##
###
Hopf maps as static solutions of the complex eikonal equation

2004
*
Journal of Mathematical Physics
*

We demonstrate that a class

doi:10.1063/1.1792931
fatcat:lhmuqk4givdazmawmnbcro7oue
*of*torus-shaped Hopf maps with arbitrary linking number obeys*the*static complex*eikonal**equation*. ... As this*equation*shows up as an integrability condition in certain non-linear field theories,*the*existence*of*such solutions is*of*some interest. ... At this point it is*of*interest to briefly consider*the**symmetries**of**the*complex static*eikonal**equation*(2) . ...##
###
Knot soliton models, submodels, and their symmetries
[article]

2005
*
arXiv
*
pre-print

Here we investigate

arXiv:hep-th/0511209v1
fatcat:q7olm66hd5etxmy6urkmickrom
*the**symmetries**of**the*submodels, where in some cases we find a*symmetry*enhancement for*the*submodels, whereas in others we do not. ... Further, CA acknowledges support from*the*Austrian START award project FWF-Y-137-TEC and from*the*FWF project P161 05 NO 5*of*N.J. Mauser. ... Acknowledgments This research was partly supported by MCyT(Spain) and FEDER (FPA2002-01161), Incentivos from Xunta de Galicia and*the*EC network "EUCLID". ...##
###
A new traveltime approximation for TI media

2012
*
Geophysics
*

By expanding

doi:10.1190/geo2011-0158.1
fatcat:525rz3immvcplbfzkz2fsyqw5i
*the*TI*eikonal**equation*in power series in terms*of**the*aneliptic parameter η, we derive an efficient tool to estimate (scan) for η in a generally inhomogeneous, elliptically anisotropic background ... In all cases,*the*accuracy*of*this new TI traveltime*equation*exceeds previously published formulations and demonstrates how η is better resolved at small offsets when*the*tilt is large. ... ACKNOWLEDGMENTS Alexey Stovas would like to acknowledge*the*ROSE project for financial support. Tariq Alkhalifah is grateful to KAUST for its support. ...##
###
A hybrid eikonal solver for accurate first-arrival traveltime computation in anisotropic media with strong contrasts
[article]

2020
*
arXiv
*
pre-print

We verify

arXiv:2008.07684v1
fatcat:j7mhkru3cjgixnhetbq3xusphi
*the*stability and accuracy*of*our hybrid*eikonal*solver using several 2D and 3D TTI medium examples. ... We develop a stable and accurate hybrid*eikonal*solver for 2D and 3D transversely isotropic media with a tilted*symmetry*axis (TTI, or tilted transversely isotropic media). ... tilt angle*of*a VTI medium's*symmetry*axis (i.e.,*the*counterclockwise rotation angle*of**the**symmetry*axis w.r.t.*the*y-axis), φ = φ(x) is*the*azimuth angle*of*a VTI medium's*symmetry*axis (i.e.,*the*...##
###
Magnetic symmetry of geometrical optics

2021
*
Qeios
*

*The*

*eikonal*

*equation*can be derived from

*the*Maxwell

*equations*\cite{born}. ... We will apply

*the*gauge potential

*of*

*the*$U(1)$ magnetic

*symmetry*to

*the*geometrical optics, especially in

*the*formulation

*of*

*eikonal*

*equation*,

*the*refractive index and

*the*curvature relation. ...

*the*

*eikonal*} \cite{landau} or \textit{

*the*optical length}, a real scalar function

*of*position \cite{born}, then

*the*

*equation*(???) ...

##
###
An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media

2015
*
Geophysics
*

Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into

doi:10.1190/geo2014-0375.1
fatcat:ryrq5632nfhw7cmztwskbcnc6m
*the**eikonal**equation*, which makes solving*the**eikonal**equation*a challenge. ... We addressed this challenge by iteratively solving a sequence*of*simpler tilted elliptically anisotropic*eikonal**equations*. ... ∂ x τÞ 2 ð c ∂ y τÞ 2 ð c ∂ z τÞ 2 ¼ 1: (6)*The*3D tilted axis*of**symmetry**eikonal**equation*For v 1 ¼ v 2 ¼ v nmo ; η 1 ¼ η 2 ¼ η; γ ¼ 1; (7)*equation*6 reduces to*the**eikonal**equation*for a TTI medium ...##
###
Pulse Propagation in Cylindrically Wound Thick Composite Specimens
[chapter]

1990
*
Review of Progress in Quantitative Nondestructive Evaluation
*

*The*findings, opinions, and recommendations expressed in this paper are those

*of*

*the*author and not necessarily those

*of*

*the*University

*of*Illinois or

*the*U.S. Navy. ... ACKNOWLEDGEMENTS This work was supported by

*the*U.S. Navy through

*the*University

*of*Illinois (Contract #N0014-86-K-0799) and was performed by

*the*Center for NDE at

*the*Ames Laboratory. ...

*The*

*eikonal*

*equations*( 4ac) have exactly

*the*same form as those for an orthotropic media

*of*cartesian

*symmetry*, where here

*the*role

*of*

*the*cartesian basis ( el' e2' e3) is played by

*the*polar basis (er ...

##
###
An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

2017
*
Geophysics
*

We have developed a 2D acoustic

doi:10.1190/geo2016-0160.1
fatcat:ozn344dcmzdxzpkeebicgo4kse
*eikonal**equation*governing*the*complex-valued traveltime*of*quasi P-waves in attenuating, transversely isotropic media with a vertical-*symmetry*axis (VTI). ... In addition, we have evaluated*the*possible extension*of**the*proposed*eikonal**equation*to realistic attenuating media, an alternative perturbation solution to*the*proposed*eikonal**equation*, and*the*feasibility ...*The*main goal*of*this paper is to develop an acoustic*eikonal**equation*for attenuating transversely isotropic media with a vertical*symmetry*axis (VTI), in which*the**symmetry**of**the*attenuation*of*waves ...
« Previous

*Showing results 1 — 15 out of 7,193 results*