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The Manley–Rowe relations are mathematical expressions developed originally for electrical engineers to predict the amount of energy in a wave that has multiple frequencies. They have since been found to describe systems in non-linear optics,fluid mechanics and the theory of non-linear dynamical systems, as they provide a pair of invariants or conserved quantities for the three-wave equation. For example, in a resonant interaction in non-linear optics, the Manley–Rowe relations can be interpreted as saying one photon is created as two more are destroyed For the three-wave equation, the Manley–Rowe invariants can be related to the modular invariants g 2 {\displaystyle g_{2}} and g 3 {\displaystyle g_{3}} of the Weierstrass ℘-function. This essentially follows because the three-wave interaction has exact solutions that are given by elliptic functions.