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Abstract

Soliton solutions of non-linear wave equations have been intensively studied as candidates to formulate elementary particles in a monistic, field-theoretical framework. The presentation reviews shortly the main theoretical background of soliton solutions. An explicit solution of a chain of elementary particles in 1+1 dimensions is constructed [I. Steinbach, arXiv:1703.05583v2, 2017]. Along the concept of 'inter-face fields' [I. Steinbach, F. Pezzolla, Physica D, 385-393, 1999], these solutions will be generalized to a 'multi-soliton network' in 1+1+2 dimensions. Based on similarities between the energy functionals in the soliton theory and the theory of superconductivity an extension to charged particles in electro-magnetic fields will be discussed.