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首页> 外文期刊>Reviews in mathematical physics >EFFECTIVE DYNAMICS FOR SOLITONS INTHE NONLINEAR KLEIN-GORDON-MAXWELLSYSTEM AND THE LORENTZ FORCE LAW
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EFFECTIVE DYNAMICS FOR SOLITONS INTHE NONLINEAR KLEIN-GORDON-MAXWELLSYSTEM AND THE LORENTZ FORCE LAW

机译：EFFECTIVE DYNAMICS FOR SOLITONS INTHE NONLINEAR KLEIN-GORDON-MAXWELLSYSTEM AND THE LORENTZ FORCE LAW

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We consider the nonlinear Klein_Gordon_Maxwell system derived from the Lagrangian _(-1/4F_μvF~μv+2/1-V(_)-eA~μJ_μ~B) on four-dimensional Minkowski space-time, where _ is a complex scalar field and F_μv=δ__A_v-δ_vA_μis the electromagnetic field. For appropriate nonlinear potentials V, the system admits soliton solutions which are gauge invariant generalizations of the non-topological soli-tons introduced and studied by Lee and collaborators for pure complex scalar fields. In this article, we develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main the_orems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field produced by the background current J~B, and compute their effective dynamics to O(e). The effective dynamical equation is the equation of motion for a relativistic particle acted on by the Lorentz force law familiar from classical electrodynamics. The theorems are valid in a scaling regime in which the external elec_tromagnetic fields are O(1), but vary slowly over space-time scales of 0(1/δ), and δ = e~l-k for k _ (0, 2/1) as e _0.We work entirely in the energy norm, and the approximation is controlled in this norm for times of 0(1/0).

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