A topological soliton is a solution of a system of partial differential equations (or alternatively, a quantum field theory), not so much because of the nature of the PDEs themselves, but because of the boundary conditions entailing the existence of homotopically distinct solutions.
Examples of topological solitons include vortices in liquid crystals, magnetic flux tubes in superconductors and domain walls in ferromagnets. Certain grand unified theories predict solitons to have formed in the early universe. According to the Big Bang theory, the universe cooled from an initial hot, dense state triggering a series of phase transitions much like what happens in condensed matter systems. Depending on the nature of symmetry breakdown various solitons are believed to have formed in the early universe according to Kibble-Higgs mechanism. The well known topological defects are magnetic monopoles, cosmic strings, domain walls, Skyrmions and textures.
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