Solitary waves for Maxwell-Dirac and Coulomb-Dirac models
Annales de l'I.H.P. Physique théorique (1998)
- Volume: 68, Issue: 2, page 229-244
- ISSN: 0246-0211
Access Full Article
topHow to cite
topAbenda, Simonetta. "Solitary waves for Maxwell-Dirac and Coulomb-Dirac models." Annales de l'I.H.P. Physique théorique 68.2 (1998): 229-244. <http://eudml.org/doc/76784>.
@article{Abenda1998,
author = {Abenda, Simonetta},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Dirac-Maxwell equation; stationary solutions},
language = {eng},
number = {2},
pages = {229-244},
publisher = {Gauthier-Villars},
title = {Solitary waves for Maxwell-Dirac and Coulomb-Dirac models},
url = {http://eudml.org/doc/76784},
volume = {68},
year = {1998},
}
TY - JOUR
AU - Abenda, Simonetta
TI - Solitary waves for Maxwell-Dirac and Coulomb-Dirac models
JO - Annales de l'I.H.P. Physique théorique
PY - 1998
PB - Gauthier-Villars
VL - 68
IS - 2
SP - 229
EP - 244
LA - eng
KW - Dirac-Maxwell equation; stationary solutions
UR - http://eudml.org/doc/76784
ER -
References
top- [1] A. Ambrosetti and P.H. Rabinowitz, Dual Variational methods in critical points theory and applications inJ. Funct. Anal., Vol. 14, 1973, pp. 349-381. Zbl0273.49063MR370183
- [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. Zbl0721.35065MR1071235
- [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. Zbl0696.35158MR968485
- [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. Zbl0465.49006MR537061
- [6] J.D. Bjorken and S.D. Drell, Relativistic quantum fields. McGraw-Hill, 1965. Zbl0184.54201MR187642
- [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. Zbl0596.35117MR847126
- [9] G. Cerami, Un criterio di esistenza per i punti critici su varietá illimitateIst. Lomb. (Rend. Sc.), Vol. A 112, 1978, pp. 332-336. Zbl0436.58006
- [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. Zbl0264.35058MR368640
- [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. Zbl0324.35076MR413833
- [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. Zbl0498.35053MR610307
- [13] M.J. Esteban, V. Georgev and E. Séré, Stationary solutions of the Maxwell-Dirac and Klein-Gordon-Dirac equations. To appear, 1995. MR1344729
- [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. Zbl0815.35103MR1309103
- [ 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. Zbl0843.35114MR1344729
- [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. Zbl0641.35064MR904136
- [17] A. Garrett Lisi, A solitary wave solution of the Maxwell-Dirac equations , University of California at San Diego, preprint 1995. Zbl0868.35121MR1364144
- [18] V. Georgiev, Small amplitude solutions of the Maxwell-Dirac equations. Indiana Univ. Math. J., Vol. 40(3), 1991, pp. 845-883. Zbl0754.35171MR1129332
- [ 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. Zbl0137.32401MR190520
- [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. Zbl0702.34039MR1079873
- [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. Zbl0541.49009
- [23] F. Merle, Existence of stationary states for nonlinear Dirac equations. J. Diff. Eq., Vol. 74(1), 1988, pp. 50-68. Zbl0696.35154MR949625
- [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. Zbl0840.34046MR1350410
- [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. Zbl0787.34041MR1137618
- [28] C. Troestler and M. Willem, Nontrivial solution of a semilinear Schrödinger equation, 1994 to appear. Zbl0864.35036MR1410836
- [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. Zbl0856.49001MR1400007
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.