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Reference.org
Three-wave equation
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<p>In <a href="/facts/Nonlinear_systems/4aYItALC">nonlinear systems</a>, the three-wave equations, sometimes called the three-wave resonant interaction equations or triad resonances, describe small-amplitude waves in a variety of non-linear media, including electrical circuits and <a href="/facts/Non-linear_optics/maerngXd">non-linear optics</a>. They are a set of three <a href="/facts/Completely_integrable/Crgzjw6G">completely integrable</a> nonlinear <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equations</a>. Because they provide the simplest, most direct example of a <a href="/facts/Resonant_interaction/EWTsxeKM">resonant interaction</a>, have broad applicability in the sciences, and are completely integrable, they have been intensively studied since the 1970s. </p>