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A Bogomolny bound rewrites a field-theory energy as a sum of nonnegative squares plus a topological term. Configurations satisfying the resulting first-order <Bogomolny equations> saturate the bound.


Bogomolny bound

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Bogomolny equations are first-order field equations obtained by setting every nonnegative square in a <Bogomolny bound> to zero. Their solutions automatically satisfy the corresponding second-order Euler-Lagrange equations.

= Bogomolny equation
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 Incoming links: Bogomolny equations