Existence of ground states for a one-dimensional relativistic schrödinger equation
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 se...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222488_v53_n6_p_Borgna http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v53_n6_p_Borgna_oai |
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I28-R145-paper_00222488_v53_n6_p_Borgna_oai2020-10-19 Borgna, J.P. Rial, D.F. 2012 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. Fil:Borgna, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rial, D.F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00222488_v53_n6_p_Borgna info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Phys. 2012;53(6) Existence of ground states for a one-dimensional relativistic schrödinger equation info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v53_n6_p_Borgna_oai |
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Universidad de Buenos Aires |
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I-28 |
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R-145 |
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Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| description |
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. |
| format |
Artículo Artículo publishedVersion |
| author |
Borgna, J.P. Rial, D.F. |
| spellingShingle |
Borgna, J.P. Rial, D.F. Existence of ground states for a one-dimensional relativistic schrödinger equation |
| author_facet |
Borgna, J.P. Rial, D.F. |
| author_sort |
Borgna, J.P. |
| title |
Existence of ground states for a one-dimensional relativistic schrödinger equation |
| title_short |
Existence of ground states for a one-dimensional relativistic schrödinger equation |
| title_full |
Existence of ground states for a one-dimensional relativistic schrödinger equation |
| title_fullStr |
Existence of ground states for a one-dimensional relativistic schrödinger equation |
| title_full_unstemmed |
Existence of ground states for a one-dimensional relativistic schrödinger equation |
| title_sort |
existence of ground states for a one-dimensional relativistic schrödinger equation |
| publishDate |
2012 |
| url |
http://hdl.handle.net/20.500.12110/paper_00222488_v53_n6_p_Borgna http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00222488_v53_n6_p_Borgna_oai |
| work_keys_str_mv |
AT borgnajp existenceofgroundstatesforaonedimensionalrelativisticschrodingerequation AT rialdf existenceofgroundstatesforaonedimensionalrelativisticschrodingerequation |
| _version_ |
1766026601189867520 |