Solitons in Three Space Dimensions as a Model for Relativistic Particles
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.
KeywordsSolitary Wave Relativistic Particle Multiplicity Result Nonlinear Functional Analysis Topological Constraint
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- 5.Benci V., Fortunato D., Masiello A., Pisani L. (1999): Solitons 1 and electromagnetic field. Math. Z., 73–102Google Scholar
- 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.Benci V., Giannoni F., Piccione P. (2000): Solitons on manifolds. Advances in Differential Equations, in pressGoogle Scholar
- 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