Topological defect

Topologically stable solution of a partial differential equation.

In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons won't decay, dissipate, disperse or evaporate in the way that ordinary waves might. The stability arises from an obstruction to the decay, which is explained by having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to continuously transform the system with a soliton in it, to one without it. The mathematics behind topological stability is both deep and broad, and a vast variety of systems possessing topological stability have been described. This makes categorization somewhat difficult.

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