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Inverse medium scattering for a nonlinear Helmholtz equation

Journal of Mathematical Analysis and Applications, 2022
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space.
Roland Griesmaier, Rainer Mandel
exaly   +3 more sources

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Linear and Nonlinear Inverse Scattering

SIAM Journal on Applied Mathematics, 1998
The authors consider the inverse scattering problem for the one-dimensional Helmholtz equation when the nonhomogeneity is confined to a half-line. A layer-stripping algorithm is developed to recover the index of refraction when the reflection coefficient is known.
Dale P. Winebrenner, John Sylvester 0002
openaire   +2 more sources

Nonlinear scattering for a system of nonlinear Klein–Gordon equations

Journal of Mathematical Physics, 2008
We consider the initial value problem for systems of nonlinear Klein–Gordon equations with quadratic nonlinearities. We prove the existence of scattering states, namely, the asymptotic stability of small solutions in the neighborhood of the free solutions for small initial data in the weighted Sobolev space H4,3(R3)×H3,3(R3).
Hayashi, Nakao, Naumkin, Pavel I., Wibowo, Ratno Bagus Edy   +2 more
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Nonlinear light scattering

Journal de Chimie Physique, 1967
Author Institution: Scientific Laboratory, Ford Motor Company P. O.
R. W. Terhune, P. D. Maker
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Chaotic scattering of waves from nonlinear scatterers

Acta Mechanica, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Moon, F. C., Raggio, G.
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Classical Theory of Nonlinear Compton Scattering

Physical Review Letters, 1996
The covariant dynamics of a single classical electron subjected to the electromagnetic field of an intense, linearly polarized, ultrashort laser pulse in vacuum is studied in the context of the Dirac-Lorentz equation, which has long been suggested as a possible theory which includes radiative reaction.
, Hartemann, , Kerman
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A Nonlinear Difference Scheme and Inverse Scattering

Studies in Applied Mathematics, 1976
A nonlinear partial difference equation is obtained and solved by the method of inverse scattering. In a certain continuum limit it is shown how this equation approximates the nonlinear Schrodinger equation and a related nonlinear differential‐difference equation.
Ablowitz, M. J., Ladik, J. F.
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