M. J. Esteban, V. Georgiev and E. S'er'e, Stationary solutions of the Maxwell--Dirac and the Klein--Gordon--Dirac equations, Calc. Var. Partial Differential Equations, 4 (1996), no. 3, 265--281 Home/Search Document Not in Database Summary Related Articles Check |
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The Dirac equation without spinors - Elton, Vassiliev (Correct)
....to spinors can be explained (at least in Minkowski 3 space) using simple tensor models. This observation may be useful in relation to attempts at modelling the electron as a soliton like solution of some nonlinear system of partial differential equations. The usual approach, see, e.g. W] and [EGS], involves the so called Maxwell Dirac equation. In our view, it might make sense looking also at other nonlinear systems which do not necessarily have spinors occurring explicitly but may still produce spinor effects. With this goal in mind, let us compare our model equation (1.2) with the ....
M. J. Esteban, V. Georgiev and E. S'er'e, Stationary solutions of the Maxwell--Dirac and the Klein--Gordon--Dirac equations, Calc. Var. Partial Differential Equations, 4 (1996), no. 3, 265--281
Solitary Waves for Maxwell-Schrödinger Equations - Coclite, Georgiev (2003) Self-citation (Georgiev) (Correct)
....the critical points of F (u, #) The first natural question is connected with the simplest case V 0 (that is z = 0) namely 2 #u = #u, x . 1. 10) It is well known that the similar physical model of Maxwell Dirac system with zero external field admits solitary solutions (see [13]) i.e. nontrivial solutions in the Schwartz class S(R ) Our first result is the following. Theorem 1.1. Let (u, #, #) be a solution of (1.10) such that u, # radial and #. 0. The above result shows that the Schrodinger Maxwell equations with zero potential have only the ....
....particle lives in a bounded space region# . Moreover, the Maxwell equations coupled with nonlinear Klein Gordon equation, with Dirac equation, with nonlinear Schrodinger equation and with the Schrodinger equation under the action of some external potential have been studied respectively in [7, 13, 9, 10, 11]. Finally we recall the classical papers [4, 5, 12] The plan of the work is the following. In Section 2 we prove some preliminary variational results, that permit to reduce (1.7) to a single equation. Moreover we show the variational structure of the problem. In Section 3 we prove some topological ....
M. J. Esteban, V. Georgiev, E. Sere, Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations, Calc. Var. 4 (1996), 265-281.
The Dirac equation without spinors - Daniel Elton Dmitri (Correct)
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M. J. Esteban, V. Georgiev and E. S'er'e, Stationary solutions of the Maxwell--Dirac and the Klein--Gordon--Dirac equations, Calc. Var. Partial Differential Equations, 4 (1996), no. 3, 265--281
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