Solitary waves for Maxwell-Dirac and Coulomb-Dirac models
Abenda, Simonetta
Annales de l'I.H.P. Physique théorique, Tome 69 (1998), p. 229-244 / Harvested from Numdam
Publié le : 1998-01-01
@article{AIHPA_1998__68_2_229_0,
     author = {Abenda, Simonetta},
     title = {Solitary waves for Maxwell-Dirac and Coulomb-Dirac models},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {69},
     year = {1998},
     pages = {229-244},
     mrnumber = {1618672},
     zbl = {0907.35104},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1998__68_2_229_0}
}
Abenda, Simonetta. Solitary waves for Maxwell-Dirac and Coulomb-Dirac models. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) pp. 229-244. http://gdmltest.u-ga.fr/item/AIHPA_1998__68_2_229_0/

[1] A. Ambrosetti and P.H. Rabinowitz, Dual Variational methods in critical points theory and applications in J. Funct. Anal., Vol. 14, 1973, pp. 349-381. | MR 370183 | Zbl 0273.49063

[2] M. Balabane, T. Cazenave and L. Vazquez, Existence of standing waves for Dirac fields with singular nonlinearities. Comm. Math. Phys., Vol. 133, 1990, pp. 53-74. | MR 1071235 | Zbl 0721.35065

[3] M. Balabane, T. Cazenave, A. Douady and F. Merle, Existence of excited states for a nonlinear Dirac field., Comm. Math. Phys., 119, 1988, pp. 153-176. | MR 968485 | Zbl 0696.35158

[4] M. Beals and M. Bezard, Solutions faibles sous des conditions d'énergie pour des équations de champ.

[5] V. Benci and P.H. Rabinowitz, Critical point theorems for indefinite functionals. Inv. Math., Vol. 52, 1979, pp. 336-352. | MR 537061 | Zbl 0465.49006

[6] J.D. Bjorken and S.D. Drell, Relativistic quantum fields. McGraw-Hill, 1965. | MR 187642 | Zbl 0184.54201

[7] T. Cazenave, On the existence of stationary states for classical nonlinear Dirac fields. In Hyperbolic systems and Mathematical Physics. Textos e Notas, Vol. 4, CMAF, Lisbonne, 1989.

[8] T. Cazenave and L. Vazquez, Existence of localized solutions for a classical nonlinear Dirac field. Comm. Math. Phys., Vol. 105, 1986, pp. 35-47. | MR 847126 | Zbl 0596.35117

[9] G. Cerami, Un criterio di esistenza per i punti critici su varietá illimitate Ist. Lomb. (Rend. Sc.), Vol. A 112, 1978, pp. 332-336. | Zbl 0436.58006

[10] J. Chadam, Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac system in one space dimension. J. Funct. Anal., Vol. 13, 1973, pp. 173-184. | MR 368640 | Zbl 0264.35058

[11] J. Chadam and R. Glassey, On the Maxwell-Dirac equations with zero magnetic field and their solutions in two space dimension. J. Math. Anal. Appl., Vol. 53, 1976, pp. 495-507. | MR 413833 | Zbl 0324.35076

[12] Y. Choquet-Bruhat, Solutions globales des équations de Maxwell-Dirac-Klein-Gordon (masses nulles). C.R. Acad. Sci. Paris, Série I, Vol. 292, 1981, pp. 153-158. | MR 610307 | Zbl 0498.35053

[13] M.J. Esteban, V. Georgev and E. Séré, Stationary solutions of the Maxwell-Dirac and Klein-Gordon-Dirac equations. To appear, 1995. | MR 1344729

[14] M.J. Esteban and E. Séré, Existence de solutions stationnaires pour l'équation de Dirac non-linéaire et le système de Dirac-Poisson. To appear in C. R. Acad. Sci., Série I, 1994. | MR 1309103 | Zbl 0815.35103

[ 15] M.J. Esteban and E. Séré, Stationary states of the nonlinear Dirac equation : a variational approach. Comm. Math. Phys., Vol. 171, 1995, pp. 323-348. | MR 1344729 | Zbl 0843.35114

[16] M. Flato, J. Simon and E. Taflin, On the global solutions of the Maxwell-Dirac equations. Comm. Math. Physics, Vol. 113, 1987, pp. 21-49. | MR 904136 | Zbl 0641.35064

[17] A. Garrett Lisi, A solitary wave solution of the Maxwell-Dirac equations , University of California at San Diego, preprint 1995. | MR 1364144

[18] V. Georgiev, Small amplitude solutions of the Maxwell-Dirac equations. Indiana Univ. Math. J., Vol. 40(3), 1991, pp. 845-883. | MR 1129332 | Zbl 0754.35171

[ 19] W.T. Grandy Jr., Relativistic Quantum Mechanics of Leptons and Fields. Kluwer Acad. Publisher, Fund. Theories of Physics, Vol. 41.

[20] L. Gross, The Cauchy problem for the coupled Maxwell and Dirac equations. Comm. Pure Appl. Math., Vol. 19, 1966, pp. 1-5. | MR 190520 | Zbl 0137.32401

[21 ] H. Hofer and Wysocki, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann., Vol. 288 (1990, pp. 483-503. | MR 1079873 | Zbl 0702.34039

[22] P.-L. Lions, The concentration-compactness method in the Calculus of Variations. The locally compact case. Part. I: Anal. non-linéaire, Ann. IHP, Vol. 1, 1984, pp. 109-145. Part. II: Anal. non-linéaire, Ann. IHP, Vol. 1, 1984, pp. 223-283. | Numdam | Zbl 0541.49009

[23] F. Merle, Existence of stationary states for nonlinear Dirac equations. J. Diff. Eq., Vol. 74(1), 1988, pp. 50-68. | MR 949625 | Zbl 0696.35154

[24] A.F. Rañada, Classical nonlinear Dirac field models of extended particles. In Quantum theory, groups, fields and particles (editor A.O. Barut). Reidel, Amsterdam, 1982.

[25] E. Séré, Homoclinic orbits on compact hypersurfaces in R2N, of restricted contact type. Comm. Math. Phys., Vol. 172, 1995, pp. 293-313. | MR 1350410 | Zbl 0840.34046

[26] M. Soler, Phys. Rev. D1, 1970, pp. 2766-2769.

[27] K. Tanaka, Homoclinic orbits in a first order superquadratic Hamiltonian system : convergence of subharmonics. Journ. Diff. Eq., Vol. 94, 1991, pp. 315-339. | MR 1137618 | Zbl 0787.34041

[28] C. Troestler and M. Willem, Nontrivial solution of a semilinear Schrödinger equation, 1994 to appear. | MR 1410836 | Zbl 0864.35036

[29] M. Wakano, Intensely localized solutions of the classical Dirac-Maxwell field equations. Progr. Theor. Phys., Vol. 35(6), 1966, pp. 1117-1141.

[30] M. Willem, Minimax theorems, to appear. | MR 1400007