## Problems in coherent wave-wave interactions in a plasma |

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3-wave inter 3-wave interactions analytic solutions angular momentum density anisotropic assumed coherent colinear complex components conservation laws consider Coupled 3-Wave Interactions coupled equations decay instability defined derived Dewar displacement vector divergent solutions dot product dynamic equation electric field energy and momentum energy density energy-momentum tensor example Figure finite frequency function gauge invariant group velocity Hence identified infinitesimal interacting waves ion beams isotropic medium Karplyuk Lagrangian Landau damping longitudinal waves magnitude Maxwell's equations negative energy waves nonlinear nonlinear interaction obtained occur Oraevskii orbital angular momentum order in smallness oscillation parameters particles phase photon physical plane waves polarization vectors possible problem Real Roots represented resonance conditions result rotations second order Section solution regions Solutions X(t space spin angular momentum Spin Balance Equations spin density spin is conserved subcases torque density total angular momentum transverse modes transverse waves triplet variables wave packet wave-wave interactions Wilhelmsson zero