Decay for travelling waves in the Gross-Pitaevskii equation
Gravejat, Philippe
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004), p. 591-637 / Harvested from Numdam
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@article{AIHPC_2004__21_5_591_0,
     author = {Gravejat, Philippe},
     title = {Decay for travelling waves in the Gross-Pitaevskii equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {21},
     year = {2004},
     pages = {591-637},
     doi = {10.1016/j.anihpc.2003.09.001},
     zbl = {1057.35060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_5_591_0}
}

Gravejat, Philippe. Decay for travelling waves in the Gross-Pitaevskii equation. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 591-637. doi : 10.1016/j.anihpc.2003.09.001. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_5_591_0/

[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. | Numdam | MR 1669387 | Zbl 0933.35177

[2] F. Béthuel, J.C. Saut, Travelling waves for the Gross-Pitaevskii equation II, in preparation.

[3] F. Béthuel, G. Orlandi, D. Smets, Vortex rings for the Gross-Pitaevskii equation, J. Eur. Math. Soc., in press. | Zbl 1091.35085

[4] Bona J.L., Li Yi A., Decay and analyticity of solitary waves, J. Math. Pures Appl. (9) 76 (5) (1997) 377-430. | MR 1460665 | Zbl 0878.35098

[5] Cianchi A., Pick L., Sobolev embeddings into BMO, VMO and L∞, Ark. Mat. 36 (2) (1998) 317-340. | Zbl 1035.46502

[6] De Bouard A., Saut J.C., Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves, SIAM J. Math. Anal. 28 (5) (1997) 1064-1085. | MR 1466669 | Zbl 0889.35090

[7] Duoandikoetxea J., Fourier Analysis, Graduate Studies in Mathematics, vol. 29, American Mathematical Society, Providence, RI, 2001. | MR 1800316 | Zbl 0969.42001

[8] Farina A., From Ginzburg-Landau to Gross-Pitaevskii, Monatsh. Math. 139 (4) (2003) 265-269. | MR 2001707 | Zbl 01984992

[9] Gravejat P., Limit at infinity for the travelling waves in the Gross-Pitaevskii equation, C. R. Math. Acad. Sci. Paris 336 (2) (2003) 147-152. | MR 1969569 | Zbl 01907785

[10] P. Gravejat, A non-existence result for supersonic travelling waves in the Gross-Pitaevskii equation, Comm. Math. Phys., in press. | MR 2020221 | Zbl 1044.35087

[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] Lizorkin P.I., Multipliers of Fourier integrals, Proc. Steklov Inst. Math. 89 (1967) 269-290. | Zbl 0167.12404

[13] M. Maris, Sur quelques problèmes elliptiques non-linéaires, Thesis of University Paris XI Orsay, 2001.

[14] Maris M., Analyticity and decay properties of the solitary waves to the Benney-Luke equation, Differential Integral Equations 14 (3) (2001) 361-384. | MR 1799899 | Zbl 1034.35123

[15] Peetre J., New Thoughts on Besov Spaces, Duke University Mathematics Series, vol. 1, Mathematics Department, Duke University, Durham, NC, 1976. | MR 461123 | Zbl 0356.46038

[16] Schwartz L., Analyse IV, Applications à la théorie de la mesure, Hermann, Paris, 1993. | Zbl 0920.00003

[17] Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Mathematical Series, vol. 32, Princeton University Press, Princeton, NJ, 1971. | MR 304972 | Zbl 0232.42007

[18] Triebel H., Theory of Function Spaces, Monographs in Mathematics, vol. 78, Birkhäuser Verlag, Basel, 1983. | MR 781540 | Zbl 0546.46027