Starting from the Vlasov-Maxwell equations by using the method of Self-Consistent field theory, we set up first the coupling relation between distribution function and density of low-frequency oscillating particles and high-frequency EF, low-frequency MF in fourier representation. Then, in the time-space representation, a set of equations for the nonlinear interaction including the effects of magnetic field generation, pondermotive force and Landau damping were derived through the expansion of the low-frequency linear dielectric function under various approximations. Finally, we also gave the Lagrangian density and conserved quantities and discussed briefly whether the magnetic field can promote the formation of soliton in three dimensions.
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