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Energetic Stability Criterion for a Nonlinear Spinorial Model

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1983-04-25
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American Physical Society
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The time evolution of expanded and contracted solitary waves of the Dirac field with scalar self-interaction is exhibited. It is shown that the positivity of the second variation of the energy functional is not a necessary condition for the stability of these waves as has been recently suggested.
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© 1983 The American Physical Society. We wish to thank Dr. J. Guasp and Dr. A. I.opez Fraguas for their help, and acknowledge the partial financial support from Instituto de Estudios Nucleares, Junta de la Energia Nulcear.
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1 V. G. Makhankov, Phys. Rep. 35, 1 (1978). 2 I. L. Bogolubsky, Phys. Lett. 73A, 87 (1979); J.Werle, Acta Phys. Pol. B 12, 601 (1981). 3 Q. N. Derrick, J. Math. Phys. (N.Y.) 5, 1252 (1964). See especially Sec. 3b. 4 A. F. Ranada, in Quantum Theory, Groups, Fields, and Particles, edited by A. O. Barut (Reidel, Dordrecht, Netherlands, 1982). 5 M. Soler, University of Zaragoza Report No. GIFT 10/75 (unpublished) . 6 The claim of soliton instability contained in the first paper of;Ref. 2 is obviously due to the use of a defective numerical scheme. Convergence of the numerical methods used in both this Letter and A. Álvarez and B. Carreras, Phys. Lett. 85A, 327 (1981), is proved by A. Álvarez, Kuo Pen-Yu, and L. Vázquez, "The Numerical Study of a Nonlinear One-Dimensional Dirac Equation" (to be published). 7 D. J. Gross and A. Neveu, Phys. Bev. D 10, 3235 (1974). 8 S. Y. Lee, T. K. Kuo, and A. Gaurielides, Phys. Rev. D 12, 2249 (1975);P. Kaus, Phys. Rev. D 14, 1722 (1976). 9 Álvarez and Carreras, Ref. 6. 10 R. J. Finkelstein, C. Fronsdal, and P. Kaus, Phys. Rev. 103, 1571 (1956). 11 M. Soler, Phys. Bev. D 1, 2766 (1970). 12 L. García and A. F. Rañada, Prog. Theor. Phys. 64, 671 (1980),and references therein.
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