Prog. Theor. Phys. Vol. 75 No. 4 (1986) pp. 953-968

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Examples of Static Localized Solutions of Nonlinear Equations in 3+1 Dimensions. II

— Asymptotic Analysis —

Minoru Umezawa

Centre de Recherches Nucléaires, Université Louis Pasteur, 67037 Strasbourg

(Received May 27, 1985)

Abstract:

A scaling operator conserved by self-interacting nonlinear system, is introduced. Solutions of nonlinear equations, introduced in a previous article, are analysed with respect to their scaling properties. As a result, the solutions can be classified into two categories according to whether they are invariant for scalig or not. The ones which are not invariant for scaling are perturbative solutions. The other class of solutions are characteristic functions of the scaling operator with vanishing characteristic value and are non-perturbative. These are isolated solutions suitable for describing elementary particles.

URL : http://ptp.ipap.jp/link?PTP/75/953/
DOI : 10.1143/PTP.75.953

References:

M. Umezawa, Prog. Theor. Phys. 75 (1986), 474[PTP].
T. H. R. Shyrme, Nucl. Phys. 31 (1962), 556[CrossRef].
For example, T. D. Lee and G. C. Wick, Phys. Rev. D9 (1974), 2291[APS].
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (London, Academic Press, 1965).
P. M. Morse and H. Feshbach, Methods of Theoretical Physics (Mc Graw-Hill Book Company INC, 1953), Part II.

Citing Article(s) :

Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1231-1249 :
Examples of Static Localized Solutions of Nonlinear Equations in 3+1 Dimensions. III

Minoru Umezawa