A topological soliton, also called a topological defect, is any solution of a set of partial differential equations that is stable against decay to the "trivial solution". Soliton stability is due to topological constraints, rather than integrability of the field equations. The constraints arise almost always because the differential equations must obey a set of boundary conditions, and the boundary has a nontrivial homotopy group, preserved by the differential equations. Thus, the differential equation solutions can be classified into homotopy classes.
a topological soliton also called a topological defect is any solution of a set of partial differential equations that is stable against decay to the "trivial solution" soliton stability is due to topological constraints rather than integrability of the field equations the constraints arise almost always because the differential equations must obey a set of boundary conditions and the boundary has a nontrivial homotopy group preserved by the differential equations thus the differential equation solutions can be classified into homotopy classes