no. 2
Travelling waves for the Gross-Pitaevskii equation I
Bethuel, Fabrice ; Saut, Jean-Claude1
1 UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France.
Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 2, pp. 147-238.
Bethuel, Fabrice  ; Saut, Jean-Claude 1

1 UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405 Orsay, France. 
@article{AIHPA_1999__70_2_147_0,
     author = {Bethuel, Fabrice and Saut, Jean-Claude},
     title = {Travelling waves for the {Gross-Pitaevskii} equation {I}},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {147--238},
     publisher = {Gauthier-Villars},
     volume = {70},
     number = {2},
     year = {1999},
     mrnumber = {1669387},
     zbl = {0933.35177},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1999__70_2_147_0/}
}
TY  - JOUR
AU  - Bethuel, Fabrice
AU  - Saut, Jean-Claude
TI  - Travelling waves for the Gross-Pitaevskii equation I
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1999
SP  - 147
EP  - 238
VL  - 70
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1999__70_2_147_0/
LA  - en
ID  - AIHPA_1999__70_2_147_0
ER  - 
%0 Journal Article
%A Bethuel, Fabrice
%A Saut, Jean-Claude
%T Travelling waves for the Gross-Pitaevskii equation I
%J Annales de l'I.H.P. Physique théorique
%D 1999
%P 147-238
%V 70
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1999__70_2_147_0/
%G en
%F AIHPA_1999__70_2_147_0
Bethuel, Fabrice; Saut, Jean-Claude. Travelling waves for the Gross-Pitaevskii equation I. Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 2, pp. 147-238. http://archive.numdam.org/item/AIHPA_1999__70_2_147_0/

[AB] L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equation, J. Math. Pures Appl., 77, 1998, pp. 1-49. | MR | Zbl

[BBH] F. Bethuel, H. Brézis and F. Hélein, Ginzburg-Landau vortices, Birkhaüser 1994. | MR | Zbl

[BCL] H. Brézis, J.-M. Coron and E. Lieb, Harmonic maps with defects, Comm. Math. Phys., 107, 1986, pp. 649-705. | MR | Zbl

[BMR] H. Brézis, F. Merle and T. Rivière, Quantization effects for -Δv = v(1 - |v|2) in R2, Arch. Rational Mech. Anal., 126, 1994, pp. 35-58. | MR | Zbl

[BR] F. Bethuel and T. Rivière, Vortices for a minimization problem related to superconductivity, Annales IHP, Analyse Non Linéaire, 12, 1995, pp. 243-303. | Numdam | MR | Zbl

[BS] F. Bethuel and J.-C. Saut, Travelling waves for the Gross-Pitaevskii equation II, in preparation.

[CJ] J.E. Colliander and R.L. Jerrard, Vortex dynamics for the Ginzburg-Landau-Schrödinger equation, Preprint, 1997. | MR

[CLMS] R. Coifman, P.-L. Lions, Y. Meyer and S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appl., 72, 1993, pp. 247-286. | MR | Zbl

[E] I. Ekeland, Convexity methods in Hamiltonian Mechanics, Springer-Verlag, 1990. | MR | Zbl

[GR] J. Grant and P.H. Roberts, Motions in a Bose condensate III, The structure and effective masses of charged and uncharged impurities, J. Phys. A. : Math. Nucl. Gen., 7, 2, 1974, pp. 260-279.

[GhP] N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points, Annales IHP, Analyse non Linéaire, 6, 1989, pp. 321-330. | Numdam | MR | Zbl

[H] F. Helein, Applications harmoniques, lois de conservation et repères mobiles, Diderot éd., Paris, 1996.

[JPR] C.A. Jones S. J. Putterman and P.H. Roberts,Motions in a Bose condensate : V. Stability of Solitary wave solutions of nonlinear Schrödinger equations in two and three dimensions, , J. Phys. A. Math. Gen., 15, 1982, pp. 2599-2619.

[JR] C.A. Jones and P.H. Roberts, Motions in a Bose condensate IV. Axisymmetric solitary waves J. Phys. A. Math. Gen., 15, 1982, pp. 2599-2619.

[K1] T. Kato, On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique, 46, 1, 1987, pp. 113-129. | Numdam | MR | Zbl

[K2] T. Kato, Nonlinear Schrödinger equations, Lecture Notes in Physics, vol. 345, Springer Verlag, Berlin, 1989, pp. 218-263. | MR | Zbl

[KR1] E.A. Kuznetsov and J.J. Rasmussen, Instability of two-dimensional solitons and vortices in defocusing media, Phys. Rev. E, 51, 5, 1995, pp. 4479-4484.

[KR2] E.A. Kuznetsov and J.J. Rasmussen, Self-focusing Instability of two-dimensional solitons and vortices, JETP, Lett., Vol. 62, 2, 1995, pp. 105-112.

[L1] F.H. Lin, Solutions of Ginzburg equations and critical points of the renormalized energy, Annales IHP, Analyse Non Linéaire, 12, 1995, pp. 599-622 | Numdam | MR | Zbl

[L1] F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math.. | MR | Zbl

[PN] K.M. Pismen and A.A. Nepomnyashchy, Stability of vortex maps in a model of superflow, Physica, D 69, 1993, pp. 163-175. | Zbl

[PR] L.M. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model, Physica D 47, 1991, pp. 353-360. | MR | Zbl

[Str] M. Struwe, On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions, J. Diff. Int. Eq., 7, 1994, pp. 1617-1624 ; Erratum J. Diff. Int. Eq., 8, 1995, p. 224. | MR | Zbl