Bogomol'nyi Prasad Sommerfield bound

The Bogomol'nyi Prasad Sommerfield bound refers to 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 is satisfied (called "saturated"), we can come up with a simpler set of partial differential equations to solve.

Examples:

• See Instanton
• Incomplete: Yang-Mills-Higgs partial differential equations.