Advertisement

Solitons in Three Space Dimensions as a Model for Relativistic Particles

  • L. Pisani
Conference paper

Abstract

This paper gives a short report of research carried out in the last five years on the existence of solitons in three space dimensions.

Benci, Fortunato and Pisani have developed a model equation proposed in 1964 by C. H. Derrick. Using some recent techniques of nonlinear functional analysis, the existence of a non-trivial solitary wave, with a topological constraint, has been proved.

Subsequent research has demonstrated the relativistic behaviour of these waves, multiplicity results and the interaction with the electromagnetic field.

Keywords

Solitary Wave Relativistic Particle Multiplicity Result Nonlinear Functional Analysis Topological Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Enz U. (1963): Discrete mass, elementary length and a topological invariant as a consequence of a relativistic invariant variational principle. Phys. Rev. 131, 1932–1934MathSciNetCrossRefGoogle Scholar
  2. 2.
    Lamb G.L. (1980): Elements of soliton theory. Wiley, New YorkMATHGoogle Scholar
  3. 3.
    Derrick C.H. (1964): Comments on nonlinear wave equations as model for elementary particles. Jour. Math. Phys. 5, 1252–1254MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Benci V., Fortunato D., Pisani L. (1998): Solitons like solutions of a Lorentz invariant equation in dimension 3. Reviews in Mathematical Physics 3, 315–344MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Benci V., Fortunato D., Masiello A., Pisani L. (1999): Solitons 1 and electromagnetic field. Math. Z., 73–102Google Scholar
  6. 6.
    Benci V., Fortunato D., Pisani L. (1996): Remarks on topological solitons. Topological Methods in Nonlinear Analysis 7, 349–367MathSciNetMATHGoogle Scholar
  7. 7.
    D’Avenia P., Pisani L.: Remarks on the topological invariants of a class of solitary waves. Nonlinear Analysis T.M.A., in pressGoogle Scholar
  8. 8.
    Benci V., Giannoni F., Piccione P. (2000): Solitons on manifolds. Advances in Differential Equations, in pressGoogle Scholar
  9. 9.
    Skyrme T.H. (1961): A non linear field theory. Proc. Roy. Soc. A 260, 127–138MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    Benci V., Fortunato D. (1999): Existence of string-like soitons. Ricerche di Matematica, 48,Suppl., pp. 399–406MathSciNetMATHGoogle Scholar
  11. 11.
    Faddeev L., Niemi A.J. (1997): Stable knot-like structures in classical field theory. Nature 387, 58–61ADSCrossRefGoogle Scholar
  12. 12.
    Benci V., Fortunato D.: On the Existence of the Impossible Pilot Wave, in Proc. of Conference “Calculus of Variations and Related Topics”, March 1998, Haifa, Israel Google Scholar

Copyright information

© Springer-Verlag Italia 2000

Authors and Affiliations

  • L. Pisani

There are no affiliations available

Personalised recommendations