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We prove the existence of solitary wave solutions to the quasilinear Benney system
where 
, –1 < p < +∞ and a, γ > 0. We establish, in particular, the existence of travelling waves with speed arbitrarily large if p < 0 and arbitrarily close to 0 if 
. We also show the existence of standing waves in the case 
, with compact support if – 1 < p < 0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.
