Abstract

SOLITONS STEMS FROM THE DELICATE BALANCE OF

Brijesh N Chawda, Dr. S.B.L. Tripathi

024-030

Vol: 1, Issue: 4, 2011

A topological soliton, or 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 inerrability 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 non-trivial homotopy group, preserved by the differential equations. Thus, the differential equation solutions can be classified into homotopy classes. There is no continuous transformation that will map a solution in one homotopy class to another. The solutions are truly distinct, and maintain their integrity, even in the face of extremely powerful forces.

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