The averaged-Lagrangian method is applied to wave-wave interactions in an infinite, homogeneous, collisionless, warm magnetoplasma. The amplitudes of the waves are assumed to vary slowly in time and space, due to coupling between them. Euler-Lagrange equations are obtained from the contributions to the averaged microscopic Lagrangian second and third order in perturbation, by variation with respect to the wave amplitudes. These are the coupled-mode equations. The phase variation yields the action transfer equation. As applications of the method, coupled-mode equations are derived in explicit forms for all possible interactions among waves propagating nearly parallel, and among those propagating exactly perpendicular, to the static magnetic field. Some of the coupling coefficients are new. Where comparisons with previous iterative analyses are possible, the advantages of the method are discussed.
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