Artículo
Borgna, J.P.; Rial, D.F. "Existence of ground states for a one-dimensional relativistic schrödinger equation" (2012) Journal of Mathematical Physics. 53(6)
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Abstract:
Relativistic Schrödinger equation with a nonlinear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a significant fraction |v| < 1 of the light speed c = 1. At first, we deal with the local and global existence of solutions of the flux, and in the second term, and according to the relativistic nature of the problem, we look for boosted solitons as ψ(x, t) = eiμtφv(x - vt), where the profile φ v ∈ H 1/2 (R{double-struck}) is a minimizer of a suitable variational problem. Our proof uses a concentration-compactness-type argument. Stability results for the boosted solitons are established. © 2012 American Institute of Physics.
Registro:
| Documento: | Artículo |
| Título: | Existence of ground states for a one-dimensional relativistic schrödinger equation |
| Autor: | Borgna, J.P.; Rial, D.F. |
| Filiación: | Instituto de Ciencias, Universidad Nacional de General Sarmiento, Juan María Gutierrez 1150, Los Polvorines, Pcia de Bs. As, 1613, Argentina Dpto. de Matemática, IMAS-CONICET, FCEyN, Universidad de Buenos Aires, Intendente Guiraldes 2160, Ciudad Univ., Pabellón I, Buenos Aires C1428EGA, Argentina |
| Año: | 2012 |
| Volumen: | 53 |
| Número: | 6 |
| DOI: | http://dx.doi.org/10.1063/1.4726198 |
| Título revista: | Journal of Mathematical Physics |
| Título revista abreviado: | J. Math. Phys. |
| ISSN: | 00222488 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00222488_v53_n6_p_Borgna.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v53_n6_p_Borgna |
Referencias:
- Bellazzini, J., Ozawa, T., Visciglia, N., Ground states for semi-relativistic Schrödinger-Poisson-Slater energies e-print arXiv:1103.2649; Borgna, J.P., Stability of periodic nonlinear Schrödinger equation (2008) Nonlinear Anal. Theory, Methods Appl., 69, pp. 4252-4265. , 10.1016/j.na.2007.11.016,
- Brezis, H., (2010) Functional Analysis, Sobolev Spaces and Partial Differential Equations, , (Springer, )
- Brezis, H., Gallouet, T., Nonlinear Schrödinger evolution equations (1980) Nonlinear Anal., 4, pp. 677-671. , 10.1016/0362-546X(80)90068-1
- Frölich, J., Lars, B., Jonsson, G., Lenzmann, E., Boson stars as solitary waves (2007) Commun. Math. Phys., 274, pp. 1-30. , 10.1007/s00220-007-0272-9
- Lenzmann, E., Well-posedness for semi-relativistic Hartree equations of critical type (2007) Math. Phys., Anal. Geom., 10, pp. 43-64. , 10.1007/s11040-007-9020-9,
- Lieb, E., Loss, M., (2001) Analysis, 14. , and 2nd ed., AMS Graduate Studies in Mathematics (American Mathematical Society, Providence, RI)
- Ponce, G., On the global well-posedness of the Benjamin-Ono equation (1991) Differential Integral Equations, 4, pp. 527-542
- Reed, M., Simon, B., (1972) Methods of Modern Mathematical Physics, 2. , (Academic)
- Strauss, W.A., Existence of solitary waves in higher dimensions (1977) Commun. Math. Phys., 55, pp. 149-162. , 10.1007/BF01626517,
- Weinstein, M., Lyapunov stability of ground states of nonlinear dispersive evolutions equations (1986) Commun. Pure Appl. Math., 39, pp. 51-68. , 10.1002/cpa.3160390103,
Citas:
---------- APA ----------
Borgna, J.P. & Rial, D.F. (2012) . Existence of ground states for a one-dimensional relativistic schrödinger equation. Journal of Mathematical Physics, 53(6).http://dx.doi.org/10.1063/1.4726198
---------- CHICAGO ----------
Borgna, J.P., Rial, D.F. "Existence of ground states for a one-dimensional relativistic schrödinger equation" . Journal of Mathematical Physics 53, no. 6 (2012).http://dx.doi.org/10.1063/1.4726198
---------- MLA ----------
Borgna, J.P., Rial, D.F. "Existence of ground states for a one-dimensional relativistic schrödinger equation" . Journal of Mathematical Physics, vol. 53, no. 6, 2012.http://dx.doi.org/10.1063/1.4726198
---------- VANCOUVER ----------
Borgna, J.P., Rial, D.F. Existence of ground states for a one-dimensional relativistic schrödinger equation. J. Math. Phys. 2012;53(6).http://dx.doi.org/10.1063/1.4726198
