La matrice de Scattering pour l'opérateur de Schrödinger sur la droite réelle
Séminaire Bourbaki : vol. 1979/80, exposés 543-560, Séminaire Bourbaki, no. 22 (1981), Talk no. 557, p. 246-256
@incollection{SB_1979-1980__22__246_0,
     author = {Colin de Verdi\`ere, Yves},
     title = {La matrice de Scattering pour l'op\'erateur de Schr\"odinger sur la droite r\'eelle},
     booktitle = {S\'eminaire Bourbaki : vol. 1979/80, expos\'es 543-560},
     author = {Collectif},
     series = {S\'eminaire Bourbaki},
     publisher = {Springer-Verlag},
     number = {22},
     year = {1981},
     note = {talk:557},
     pages = {246-256},
     mrnumber = {636527},
     zbl = {0467.34019},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1979-1980__22__246_0}
}
Colin de Verdière, Y. La matrice de Scattering pour l'opérateur de Schrödinger sur la droite réelle, in Séminaire Bourbaki : vol. 1979/80, exposés 543-560, Séminaire Bourbaki, no. 22 (1981), Talk no. 557, pp. 246-256. http://www.numdam.org/item/SB_1979-1980__22__246_0/

[A] V. Arnold - Méthodes mathématiques de la mécanique classique (traduction française), MIR, 1976. | MR 474391 | Zbl 0385.70001

[A-M] Z. Agranovich and V. Marchenko - The inverse scattering theory, Gordon and Breach, New-York, 1963. | MR 162497 | Zbl 0117.06003

[B-G-M] M. Berger, P. Gauduchon et E. Mazet - Le spectre d'une variété riemannienne, Lecture Notes in Math., n° 194. | Zbl 0223.53034

[C] P. Cartier - Développements de fonctions arbitraires suivant les fonctions propres d'un opérateur différentiel, Sém. Bourbaki, exposé n° 102. | Numdam | Zbl 0121.09901

[CV 1] Y. Colin De Verdière - Propriétés asymptotiques de l'équation de la chaleur sur une variété compacte, Sém. Bourbaki, exposé n° 439. | Numdam | Zbl 0324.58019

[CV 2] Y. Colin De Verdière - Une formule de traces pour l'opérateur de Schrödinger dans R3 , Ann. E.N.S. (à paraître). | Numdam | Zbl 0482.35068

[D-T] P. Deift and E. Trubowitz - Inverse scattering on the line, CPAM 32(1979), 121-251. | MR 512420 | Zbl 0388.34005

[F] L. Faddeev - Properties of the S-matrix of the one-dimensional Schrödinger equation, AMST 2, 65(1966), 139-166. | Zbl 0181.56704

[F-Z] L. Faddeev and V. Zakharov - KdV equation : a completely integrable Hamiltonian system, Funct. Analysis and its applications 5(1971), 280-287. | Zbl 0257.35074

[G-G-K-M] C. Gardner, J. Greene, M. Kruskal and R. Miura - Method for solving the KdV equation, Phys. Rev. Letters 19(1967), 1095-1097. | Zbl 1103.35360

[G-L] I.M. Gelfand and B.M. Levitan - On the determination of a differential equation from its spectral functions, AMST 2, 1(1955), 253-304. | MR 73805 | Zbl 0066.33603

[J-K] A. Jensen and T. Kato - Asymptotic behavior of the scattering phase for exterior domains, Comm. P.D.E. 3(1978), 1165-1195. | MR 512084 | Zbl 0419.35067

[K-dV] D. Korteweg and G. De Vries - On the change of form of long waves advancing in a rectangular canal, and a new type of long stationnary waves, Philos. Mag., 39(1895), 422-443. | JFM 26.0881.02

[L 1] P. Lax - Integrals of non-linear equations of evolution and solitary waves, CPAM, 21(1968), 467-490. | MR 235310 | Zbl 0162.41103

[L 2] P. Lax - Periodic solutions of the KdV equation, CPAM, 28(1975), 141-188. | MR 369963 | Zbl 0295.35004

[L-P] P. Lax and R. Phillips - Scattering theory for automorphic functions, Annals of Math. Studies, Princeton, 1976. | MR 562288 | Zbl 0362.10022

[LN] N. Levinson - On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase, Danske Vid. Selsk. Math. Fys. Medd., 25(1944), 1-29. | MR 30080 | Zbl 0032.20702

[M] R. Miura - The KdV equation : a survey of results, SIAM Review, 18(1976), 412-457. | MR 404890 | Zbl 0333.35021

[McK] H.P. Mc Kean -Integrable systems and algebraic curves, Lecture Notes in Math. 755, 83-200. | MR 564904 | Zbl 0449.35080

[MK-M] H.P. Mckean and P. Van Moerbeke - The spectrum of Hill's equation, Invent. Math., 30(1975), 217-274. | MR 397076 | Zbl 0319.34024

[M-R] A. Majda and J. Ralston - An analogue of Weyl's theorem for unboùnded domains, I, II et III, Duke Math. Journal, 45(1978), 183-196 et 513-536, et 46(1979), 725-731. | Zbl 0416.35058

[R-S] M. Reed and B. Simon - Methods of modern mathematical physics, III : scattering theory, Academic Press, 1979. | MR 529429 | Zbl 0405.47007