Bogomol'nyi–Prasad–Sommerfield bound

The Bogomol'nyi–Prasad–Sommerfield bound (named after Evgeny Bogomolny, M.K. Prasad, and Charles Sommerfield) is a series of inequalities for solutions of partial differential equations depending on the homotopy class of the solution at infinity. This set of inequalities is very useful for solving soliton equations. Often, by insisting that the bound be satisfied (called "saturated"), one can come up with a simpler set of partial differential equations to solve the Bogomolny equations. Solutions saturating the bound are called "BPS states" and play an important role in field theory and string theory.