@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://www.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://www.numdam.org/item/AIHPA_1999__70_2_147_0/ LA - en ID - AIHPA_1999__70_2_147_0 ER -
Bethuel, Fabrice; Saut, Jean-Claude. Travelling waves for the Gross-Pitaevskii equation I. Annales de l'I.H.P. Physique théorique, Volume 70 (1999) no. 2, pp. 147-238. http://www.numdam.org/item/AIHPA_1999__70_2_147_0/
[AB] Topological methods for the Ginzburg-Landau equation, J. Math. Pures Appl., 77, 1998, pp. 1-49. | MR | Zbl
and ,[BBH] Ginzburg-Landau vortices, Birkhaüser 1994. | MR | Zbl
, and ,[BCL] Harmonic maps with defects, Comm. Math. Phys., 107, 1986, pp. 649-705. | MR | Zbl
, and ,[BMR] Quantization effects for -Δv = v(1 - |v|2) in R2, Arch. Rational Mech. Anal., 126, 1994, pp. 35-58. | MR | Zbl
, and ,[BR] Vortices for a minimization problem related to superconductivity, Annales IHP, Analyse Non Linéaire, 12, 1995, pp. 243-303. | Numdam | MR | Zbl
and ,[BS] Travelling waves for the Gross-Pitaevskii equation II, in preparation.
and ,[CJ] Vortex dynamics for the Ginzburg-Landau-Schrödinger equation, Preprint, 1997. | MR
and ,[CLMS] Compensated compactness and Hardy spaces, J. Math. Pures Appl., 72, 1993, pp. 247-286. | MR | Zbl
, , and ,[E] Convexity methods in Hamiltonian Mechanics, Springer-Verlag, 1990. | MR | Zbl
,[GR] 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.
and ,[GhP] A general mountain pass principle for locating and classifying critical points, Annales IHP, Analyse non Linéaire, 6, 1989, pp. 321-330. | Numdam | MR | Zbl
and ,[H] Applications harmoniques, lois de conservation et repères mobiles, Diderot éd., Paris, 1996.
,[JPR] 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.
. and ,[JR] Motions in a Bose condensate IV. Axisymmetric solitary waves J. Phys. A. Math. Gen., 15, 1982, pp. 2599-2619.
and ,[K1] On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique, 46, 1, 1987, pp. 113-129. | Numdam | MR | Zbl
,[K2] Nonlinear Schrödinger equations, Lecture Notes in Physics, vol. 345, Springer Verlag, Berlin, 1989, pp. 218-263. | MR | Zbl
,[KR1] Instability of two-dimensional solitons and vortices in defocusing media, Phys. Rev. E, 51, 5, 1995, pp. 4479-4484.
and ,[KR2] Self-focusing Instability of two-dimensional solitons and vortices, JETP, Lett., Vol. 62, 2, 1995, pp. 105-112.
and ,[L1] 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] Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math.. | MR | Zbl
,[PN] Stability of vortex maps in a model of superflow, Physica, D 69, 1993, pp. 163-175. | Zbl
and ,[PR] Motion of vortex lines in the Ginzburg-Landau model, Physica D 47, 1991, pp. 353-360. | MR | Zbl
and ,[Str] 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
,