The nonlinear regime of the kinetic Alfven wave is studied in a collisionle
ss low-beta plasma that is composed of a cold ion population and of two ele
ctron populations. In the one electron population plasma, it is known that
solitary kinetic Alfven waves (SKAW) propagate either at the Alfven velocit
y nu(A) or at the ion-acoustic velocity c(s). In this latter case, only pla
sma compressions exist. In the two electron population plasma, rarefactions
, as well as compressions, may exist at this velocity. Furthermore, when th
e electron-acoustic mode exists and when nu(A) > nu(ea) (nu(ea) is the elec
tron-acoustic velocity), the inertia of the cold electron component allows
for the existence of compressive SKAW which propagate with a velocity lying
in a limited interval above nu(ea),. When nu A < nu(ea), these solitons ar
e rarefactive and continuously evolve from classical SKAW moving at nu(A) t
o electron-acoustic-like SKAW moving at nu(ea). The possibility of applying
these results to some astrophysical plasma observations is investigated. (
C) 1999 American Institute of Physics. [S1070-664X(99)00302-X].