Nonlinear Resonant Interaction of Two Longitudinal Waves and a Transverse Wave in a Hot Magnetized Plasma

By Whitham's method of averaged Lagrangian and using Low's form of Lagrangian, coupled mode equations and coupling coefficients are derived for resonant nonlinear interaction of two longitudinal and one transverse wave in a magnetized plasma, in which the later wave propagates along the external uniform magnetic field. The limiting form of these coupling coefficients are obtained when the external magnetic field vanishes.