Le problème spectral inverse pour les systèmes AKNS périodiques sur la droite réelle

B. Grebert; J. C. Guillot

Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990)

  • page 1-10

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Grebert, B., and Guillot, J. C.. "Le problème spectral inverse pour les systèmes AKNS périodiques sur la droite réelle." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-10. <http://eudml.org/doc/112001>.

@article{Grebert1989-1990,
author = {Grebert, B., Guillot, J. C.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {inverse spectral problem; Dirac system; isospectral set},
language = {fre},
pages = {1-10},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Le problème spectral inverse pour les systèmes AKNS périodiques sur la droite réelle},
url = {http://eudml.org/doc/112001},
year = {1989-1990},
}

TY - JOUR
AU - Grebert, B.
AU - Guillot, J. C.
TI - Le problème spectral inverse pour les systèmes AKNS périodiques sur la droite réelle
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1989-1990
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 10
LA - fre
KW - inverse spectral problem; Dirac system; isospectral set
UR - http://eudml.org/doc/112001
ER -

References

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  1. [AKNS] M.J. Ablowitz, D.J. Kaup, A.C. Newell et H. Segur.The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math.53, (1974), p.249-315 Zbl0408.35068MR450815
  2. [Gar-Tru 1] J. Garnett et E. Trubowitz.Gaps and bands of one dimensional periodic Schrödinger operators. Comment. Math. Helvetici, 59, (1984), p.258-312. Zbl0554.34013MR749109
  3. [Gar-Tru 2] J. Garnett et E. Trubowitz.Gaps and bands of one dimensional periodic Schrödinger operators II. Comm. Math. Helvetici62, (1987), p.18-37. Zbl0649.34034MR882963
  4. [Ge-Sch-Si] Commutation methods applied to the mKdV-equation. Publication du département de Mathématiques, Université du Missouri, Columbia (1990). 
  5. [Ka] Th. Kappeler.On the periodic spectrum of the one dimensional Schrödinger equation. Comm. Math. Helvetici65, (1990), p.1-3. Zbl0703.34085MR1036124
  6. [Mar-Ost 1] V.A. Marchenko and I.V. Ostrovsky.A characterisation of the spectrum of Hill's operator. Math. USSR. Sbornik, 97, (1975), p.493-554. Zbl0343.34016
  7. [Mar-Ost 2] V.A. Marchenko and I.V. Ostrovsky.Approximation of periodic by finite-zone potentials. Selecta Math. Sovietici6, (1987), p. 101-106. Zbl0624.31005
  8. [Mis 1] T.V. Misyura.Properties of the spectra of periodic and antiperiodic boundary value problems generated by Dirac operators I, II (in Russian)Teor. Funktsü Funktsional Anal. i Prilozhen30, (1978), p.90-101; 31, (1979), p.102-109. Zbl0441.34020
  9. [Mis 2] T.V. Misyura.Finite zone Dirac operators (in Russian). Teor. Funktsü Funktsional Anal. i Prilozhen33, (1980), p. 107-111. Zbl0464.47019MR568021
  10. [Pö-Tru] J. Pöschel et E. Trubowitz.Inverse Spectral Theory. Academic Press (1987). Zbl0623.34001MR894477
  11. [Zah-Sha] V. Zakharov et A. Shabat, A scheme for integrating nonlinear equations of mathematical physics by the method of the inverse scattering problem. Func. Anal. and Appl.8, (1974), p.226-235. Zbl0303.35024

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