Foliation of phase space for the cubic non-linear Schrödinger equation

D. Bättig; B. Grébert; J. C. Guillot; T. Kappeler

Compositio Mathematica (1993)

  • Volume: 85, Issue: 2, page 163-199
  • ISSN: 0010-437X

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Bättig, D., et al. "Foliation of phase space for the cubic non-linear Schrödinger equation." Compositio Mathematica 85.2 (1993): 163-199. <http://eudml.org/doc/90196>.

@article{Bättig1993,
author = {Bättig, D., Grébert, B., Guillot, J. C., Kappeler, T.},
journal = {Compositio Mathematica},
keywords = {inverse spectral theory; integrable systems; invariant tori; defocusing nonlinear Schrödinger equation},
language = {eng},
number = {2},
pages = {163-199},
publisher = {Kluwer Academic Publishers},
title = {Foliation of phase space for the cubic non-linear Schrödinger equation},
url = {http://eudml.org/doc/90196},
volume = {85},
year = {1993},
}

TY - JOUR
AU - Bättig, D.
AU - Grébert, B.
AU - Guillot, J. C.
AU - Kappeler, T.
TI - Foliation of phase space for the cubic non-linear Schrödinger equation
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 85
IS - 2
SP - 163
EP - 199
LA - eng
KW - inverse spectral theory; integrable systems; invariant tori; defocusing nonlinear Schrödinger equation
UR - http://eudml.org/doc/90196
ER -

References

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  2. [Gar-Tru 1] J. Garnett and E. Trubowitz.Gaps and bands of one dimensional periodic Schrödinger operators. Comment. Math. Helvetici, 59, p. 258-312 (1984). Zbl0554.34013MR749109
  3. [Gar-Tru 2] J. Garnett and E. Trubowitz.Gaps and bands of one dimensional periodic Schrödinger operators II. Comment. Math. Helvetici, 62, p. 18-37 (1987). Zbl0649.34034MR882963
  4. [Gre] B. Grébert.Problèmes spectraux inverses pour les systèmes AKNS sur la droite réelle. Thèse de I'Université Paris-Nord. Mai 1990. 
  5. [Gre-Gui] B. Grébert and J.C. Guillot.Gaps of one dimensional periodic AKNS systems. Rapport du Centre de Mathématiques Appliquées de l'Ecole Polytechnique no. 215. Juin 1990. To appear in Forum Mathematicum. Zbl0784.34024MR1107987
  6. [Ka] T. Kato.Perturbation theory for linear operators. 2nd ed., Springer-Verlag, 1976. Zbl0148.12601MR407617
  7. [Kp] T. Kappeler.Foliation by the Korteweg-de Vries equation (to appear in Ann. Inst. Fourier). 
  8. [Mck-Tru] H.P. McKean, E. Trubowitz.Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points. C.P.A.M.29, p. 143-226 (1976). Zbl0339.34024MR427731
  9. [Pö-Tru] J. Pöschel and E. Trubowitz.Inverse Spectral Theory. Academic Press (1987). Zbl0623.34001MR894477
  10. [P-S] G. Polya and G. Szegö.Aufgaben und Lehrsätze aus der Analysis. Vol. 2, 3rd ed., Grundlehren, Bd 20, Springer-Verlag, New York, 1964. Zbl0122.29704
  11. [Pre] E. Previato.Hyperelliptic quasi-periodic and solitons solutions of the nonlinear Schrödinger equation. Duke Math. J.52, p. 329-377 (1985). Zbl0578.35086MR792178
  12. [Sim] B. Simon.Trace ideals. Cambridge University Press, 1979. MR541149
  13. [Tru] E. Trubowitz.The inverse problem for periodic potentials. C.P.A.M., 30, p. 321-337 (1977). Zbl0403.34022MR430403

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