Lagrangian approach to non-linear wave interactions in a warm plasma

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.