Am. Hamza, A KINETIC DERIVATION OF A GENERALIZED ZAKHAROV-KUZNETSOV EQUATION FORION-ACOUSTIC TURBULENCE IN A MAGNETIZED PLASMA, Physics letters. A, 190(3-4), 1994, pp. 309-316
The Zakharov-Kuznetsov equation has been derived by a number of author
s in the context of a fluid description as well as a kinetic descripti
on in a nonmagnetized plasma. We propose, in this short paper, to disc
uss the derivation of the equation governing the evolution of ion acou
stic waves in a magnetized plasma using kinetic theory. This allows us
to introduce Landau damping more specifically, as well as other purel
y nonlinear kinetic effects. We first investigate the effects of Landa
u damping on the conservation laws, and therefore on the solitary solu
tion known to exist in the fluid regime. We also derive a conservation
law very much like the one-dimensional case.