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 second...

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Detalles Bibliográficos
Autores: Borgna, Juan Pablo, Rial, Diego Fernando
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/125772
Acceso en línea:http://hdl.handle.net/11336/125772
Access Level:acceso abierto
Palabra clave:GROUND STATES
NONLINEAR EQUATION
SCHROEDINGER EQUATION
SOLITONS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.