Results 171 to 180 of about 16,809 (204)

Eikonal Approximation for Nonlinear Equations

Journal of Mathematical Physics, 1970
An eikonal approximation for nonlinear equations is derived from an expansion in powers of space and time derivatives. For the special case of one dependent variable, the method is equivalent to an averaging method proposed by Whitham and derived by Luke.
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Linearization of the eikonal equation

GEOPHYSICS, 1994
Seismic traveltime tomography is a nonlinear inverse problem wherein an unknown slowness model is inferred from the observed arrival times of seismic waves. Nonlinearity arises because the raypath connecting a given source and receiver depends on the slowness.
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Effective Hamiltonian and Homogenization of Measurable Eikonal Equations

Archive for Rational Mechanics and Analysis, 2006
The authors describe the homogenization of evolution Hamilton-Jacobi equations \(u_{\varepsilon t}+H(Du_{\varepsilon })=f(x/\varepsilon )\) posed in \(\mathbb R^{N}\times (0,+\infty)\). Here the potential \(f\) is supposed to be \(\mathbb Z^{N}\)-periodic, measurable and essentially bounded.
CAMILLI, FABIO, SICONOLFI, Antonio
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The two-dimensional eikonal equation

Siberian Mathematical Journal, 2006
Summary: We study the two-dimensional eikonal equation \(\psi_x^2+ \psi_y^2=1/v^2(x,y)\). We carry out the group analysis of the equation, establish a connection between the group properties and geometric characteristics of the Riemannian space with the metric \(ds^2=[dx^2+dy^2]/v^2(x,y)\).
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On Complex Solutions of the Eikonal Equation

2007 International Conference on Electromagnetics in Advanced Applications, 2007
In this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometrical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries.
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Automatic Difference Operators for the Eikonal Equation

SIAM Journal on Scientific Computing
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alex Kleb, Krzysztof J. Fidkowksi, Joaquim R. R. A. Martins   +2 more
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Singularities of Solutions of the Eikonal Equation

Differential Equations, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Eikonal approximation and the parabolic equation

The Journal of the Acoustical Society of America, 1976
We discuss two aspects of the general problem of sound propagation in an ocean characterized by a range-dependent profile. We first consider a normal-mode formalism for describing a situation in which the eikonal approximation can be applied in the horizontal plane.
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The eikonal equation

2020
Rafael G González-Acuña, Héctor A Chaparro-Romo   +1 more
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PINNeik: Eikonal solution using physics-informed neural networks

Computers and Geosciences, 2021
Umair bin Waheed, Ehsan Haghighat, Tariq Alkhalifah   +2 more
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