ONE-PARAMETER FAMILY OF SOLITON-SOLUTIONS WITH COMPACT SUPPORT IN A CLASS OF GENERALIZED KORTEWEG-DE VRIES EQUATIONS

We study the generalized Korteweg-de Vries (KdV) equations derivable f rom the Lagrangian L(l,p) = integral[1/2 phi(x) phi(t) - (phi x)(l)/l( l-1) + alpha(phi(x))(p)(phi(xx))(2)]dx, where the usual fields u(x, t) of the generaliaed KdV equation are defined by u(u, t) = phi(x)(x, t) . For p an arbitrary continuous parameter 0 < p less than or equal to 2, l = p + 2 we find soliton solutions with compact support (compacton s) to these equations which have the feature that their width is indep endent of the amplitude. This generalizes previous results which consi dered p = 1, 2. For the exact compactons we find a relation between th e energy, mass, and velocity of the solitons. We show that this relati onship can also be obtained using a variational method based on the pr inciple ofIeast action.