Coupled Klein-Gordon and Born-Infeld-type equations: Looking for solitary waves

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 460, Issue 2045, 2004, Pages 1519-1527

  Mugnai, Dimitri ^a  

^a UNIVERSITY OF PERUGIA   (Italy)

Author keywords

L a priori estimate; 2 mountain pass

Indexed keywords

ARTICLE; ELECTRIC FIELD; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICS;

EID: 2342470017     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2003.1267     Document Type: Article

References (16)

1. Avron, J., Herbst, I. & Simon, B. 1978 Schrödinger operators with electromagnetic fields. I. General interaction. Duke Math. J. 45, 847-883.
2. Avron, J., Herbst, I. & Simon, B. 1981 Schrödinger operators with electromagnetic fields. III. Atoms in homogeneous magnetic field. Commun. Math. Phys. 79, 529-572.
3. Benci, V. & Fortunato, D. 1998 An eigenvalue problem for the Schrödinger-Maxwell equations. Topolog. Meth. Nonlin. Analysis 11, 283-293.
4. Benci, V. & Fortunato, D. 2002 Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equation. Rev. Math. Phys. 14, 409-420.
5. Benci, V., Fortunato, D., Masiello, A. & Pisani, L. 1999 Solitons and electromagnetic fields. Math. Z. 232, 73-102.
6. Berestycki, H. & Lions, P. L. 1983a Nonlinear scalar field equatios. I. Existence of a ground state. Arch. Ration. Mech. Analysis 82, 313-345.
7. Berestycki, H. & Lions, P. L. 1983b Nonlinear scalar field equatios. II. Existence of infinitely many solutions. Arch. Ration. Mech. Analysis 82, 347-375.
8. Born, M. & Infeld, L. 1934 Foundations of the new field theory. Proc. R. Soc. Lond. A 144, 425-451.
9. Combes, J. M., Schrader, R. & Seiler, R. 1978 Classical bounds and limits for energy distributions of Hamiltonian operators in electromagnetic fields. Ann. Phys. 111, 1-18.
10. D'Aprile, T. & Mugnai, D. 2004 Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations. Preprint, University of Bari. (Submitted.)
11. D'Avenia, P. & Pisani, L. 2002 Nonlinear Klein-Gordon equations coupled with Born-Infeld type equations. Electron. J. Diff. Eqns 26, 1-13.
12. del Pino, M., Felmer, P. & Tanaka, K. 2002 An elementary construction of complex patterns in nonlinear Schrödinger equations. Nonlinearity 15, 1653-1671.
13. Felsager, B. 1998 Geometry, particles and fields. Springer.
14. Fortunato, D., Orsina, L. & Pisani, L. 2002 Born-Infeld type equations for electrostatic fields. J. Math. Phys. 43, 5698-5706.
15. N. C. R. Acad. Sci. Paris Sér. I 302, 673-676.
16. Rabinowitz, P. H. 1986 Minimax methods in critical point theory with applications to differential equations. Regional Conference Series in Mathematics, vol. 65. Providence, RI: American Mathematical Society.