: also see topological excitations and the base concepts: topology, differential equations, quantum mechanics & condensed matter physics. in mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of homotopically distinct solutions. typically, this occurs because the boundary on which the boundary conditions are specified has a non-trivial homotopy group which is preserved in differential equations; the solutions to the differential equations are then topologically distinct, and are classified by their homotopy class. topological defects are not only stable against small perturbations, but cannot decay or be undone or be de-tangled, precisely because there is no continuous transformation that will map them (homotopically) to a uniform or "trivial" solution. examples include the soliton or solitary wave which occurs in many exactly solvable models, the screw dislocations in crystalline materials, the skyrmion and the wessâzuminoâwitten model in quantum field theory. topological defects are believed to drive phase transitions in condensed matter physics. notable examples of topological defects are observed in lambda transition universality class systems including: screw/edge-dislocations in liquid crystals, magnetic flux tubes in superconductors and vortices in superfluids. the authenticity of a topological defect depends on the authenticity of the vacuum in which the system will tend towards if infinite time elapses; false and true topological defects can be distinguished if the defect is in a false vacuum and a true vacuum, respectively. ==cosmology== certain grand unified theories predict topological defects 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. in physical cosmology, a topological defect is an (often) stable configuration of matter predicted by some theories to form at phase transitions in the very early universe. ===symmetry breakdown=== depending on the nature of symmetry breakdown, various solitons are believed to have formed in the early universe according to the higgsâkibble mechanism. the well-known topological defects are magnetic monopoles, cosmic strings, domain walls, skyrmions and textures. as the universe expanded and cooled, symmetries in the laws of physics began breaking 
Inflation_(cosmology) Large-scale_structure_of_the_cosmos Solitons