  We prove in this paper the stability and asymptotic stability in H^1 of a
decoupled sum of N solitons for the subcritical generalized KdV equations
$u_t+(u_{xx}+u^p)_x=0$ (1<p<5). The proof of the stability result is based on
energy arguments and monotonicity of local L^2 norm. Note that the result is
new even for p=2 (the KdV equation). The asymptotic stability result then
follows directly from a rigidity theorem in [15].
