Decay for travelling waves in the Gross–Pitaevskii equation

Philippe Gravejat

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

  • Volume: 21, Issue: 5, page 591-637
  • ISSN: 0294-1449

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Gravejat, Philippe. "Decay for travelling waves in the Gross–Pitaevskii equation." Annales de l'I.H.P. Analyse non linéaire 21.5 (2004): 591-637. <http://eudml.org/doc/78631>.

@article{Gravejat2004,
author = {Gravejat, Philippe},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Nonlinear Schrödinger equation; Travelling waves; Decay at infinity},
language = {eng},
number = {5},
pages = {591-637},
publisher = {Elsevier},
title = {Decay for travelling waves in the Gross–Pitaevskii equation},
url = {http://eudml.org/doc/78631},
volume = {21},
year = {2004},
}

TY - JOUR
AU - Gravejat, Philippe
TI - Decay for travelling waves in the Gross–Pitaevskii equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 5
SP - 591
EP - 637
LA - eng
KW - Nonlinear Schrödinger equation; Travelling waves; Decay at infinity
UR - http://eudml.org/doc/78631
ER -

References

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  1. [1] Béthuel F., Saut J.C., Travelling waves for the Gross–Pitaevskii equation I, Ann. Inst. H. Poincaré Phys. Théor.70 (2) (1999) 147-238. Zbl0933.35177MR1669387
  2. [2] F. Béthuel, J.C. Saut, Travelling waves for the Gross–Pitaevskii equation II, in preparation. Zbl1190.35196
  3. [3] F. Béthuel, G. Orlandi, D. Smets, Vortex rings for the Gross–Pitaevskii equation, J. Eur. Math. Soc., in press. Zbl1091.35085
  4. [4] Bona J.L., Li Yi A., Decay and analyticity of solitary waves, J. Math. Pures Appl. (9)76 (5) (1997) 377-430. Zbl0878.35098MR1460665
  5. [5] Cianchi A., Pick L., Sobolev embeddings into BMO, VMO and L∞, Ark. Mat.36 (2) (1998) 317-340. Zbl1035.46502
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  7. [7] Duoandikoetxea J., Fourier Analysis, Graduate Studies in Mathematics, vol. 29, American Mathematical Society, Providence, RI, 2001. Zbl0969.42001MR1800316
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  9. [9] Gravejat P., Limit at infinity for the travelling waves in the Gross–Pitaevskii equation, C. R. Math. Acad. Sci. Paris336 (2) (2003) 147-152. Zbl1145.35458MR1969569
  10. [10] P. Gravejat, A non-existence result for supersonic travelling waves in the Gross–Pitaevskii equation, Comm. Math. Phys., in press. Zbl1044.35087MR2020221
  11. [11] Jones C.A., Roberts P.H., Motions in a Bose condensate IV, Axisymmetric solitary waves, J. Phys. A. Math. Gen.15 (1982) 2599-2619. 
  12. [12] Lizorkin P.I., Multipliers of Fourier integrals, Proc. Steklov Inst. Math.89 (1967) 269-290. Zbl0167.12404
  13. [13] M. Maris, Sur quelques problèmes elliptiques non-linéaires, Thesis of University Paris XI Orsay, 2001. 
  14. [14] Maris M., Analyticity and decay properties of the solitary waves to the Benney–Luke equation, Differential Integral Equations14 (3) (2001) 361-384. Zbl1034.35123MR1799899
  15. [15] Peetre J., New Thoughts on Besov Spaces, Duke University Mathematics Series, vol. 1, Mathematics Department, Duke University, Durham, NC, 1976. Zbl0356.46038MR461123
  16. [16] Schwartz L., Analyse IV, Applications à la théorie de la mesure, Hermann, Paris, 1993. Zbl0920.00003
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  18. [18] Triebel H., Theory of Function Spaces, Monographs in Mathematics, vol. 78, Birkhäuser Verlag, Basel, 1983. Zbl0546.46027MR781540

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