Inverse problem for a nonlinear Helmholtz equation

Emmanuel Jalade

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 4, page 517-531
  • ISSN: 0294-1449

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Jalade, Emmanuel. "Inverse problem for a nonlinear Helmholtz equation." Annales de l'I.H.P. Analyse non linéaire 21.4 (2004): 517-531. <http://eudml.org/doc/78628>.

@article{Jalade2004,
author = {Jalade, Emmanuel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {linear Helmholtz equation; scattering operator, scattering amplitude; Fourier transform; perturbation; nonlinear Schrödinger equation; uniqueness},
language = {eng},
number = {4},
pages = {517-531},
publisher = {Elsevier},
title = {Inverse problem for a nonlinear Helmholtz equation},
url = {http://eudml.org/doc/78628},
volume = {21},
year = {2004},
}

TY - JOUR
AU - Jalade, Emmanuel
TI - Inverse problem for a nonlinear Helmholtz equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 4
SP - 517
EP - 531
LA - eng
KW - linear Helmholtz equation; scattering operator, scattering amplitude; Fourier transform; perturbation; nonlinear Schrödinger equation; uniqueness
UR - http://eudml.org/doc/78628
ER -

References

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  1. [1] Colton D, Kreiss R, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, 1998. Zbl0760.35053MR1635980
  2. [2] Hörmander L, The Analysis of Linear Partial Differential Operators II, Springer-Verlag, 1983. Zbl0687.35002MR705278
  3. [3] Isakov V, Nachmann A, Global uniqueness for a 2-dimensional semilinear elliptic problem, Trans. Amer. Math. Soc.347 (1995) 3375-3390. Zbl0849.35148MR1311909
  4. [4] Isakov V, Sylvester J, Global uniqueness for a semilinear elliptic inverse problem, CPAM47 (1994) 1403-1410. Zbl0817.35126MR1295934
  5. [5] Nachmann A, Reconstruction from boundary measurement, Ann. Math.128 (1988) 531-577. Zbl0675.35084
  6. [6] Strauss W.A, Nonlinear scattering theory, in: La Vita J.A, Marchand J.-P (Eds.), Scattering Theory in Mathematical Physics, Reidel, Dordrecht, 1974. 
  7. [7] Weder R, Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case, Proc. Amer. Math. Soc.129 (12) (2002) 3637-3645. Zbl0986.35125MR1860498

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