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Nonlinear Dirac equation solitary waves in external fields

Opened Access Nonlinear Dirac equation solitary waves in external fields


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Autor: Mertens, Franz G.
Quintero, Niurka R.
Cooper, Fred
Khare, Avinash
Saxena, Avadh
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Fecha: 2012
Publicado en: Physical Review E, 2012, 86(4), 046602: 1-20
Tipo de documento: Artículo
Resumen: We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2κ+1(Ψ¯¯¯Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq̇ (t)<0. Here P(t) is the momentum of the soli...
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Tamaño: 2.159Mb
Formato: PDF


DOI: 10.1103/PhysRevE.86.046602

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