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 from 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 (compactons) to these equations which have the feature that their width is independent of the amplitude. This generalizes previous results which considered p = 1, 2. For the exact compactons we find a relation between the energy, mass, and velocity of the solitons. We show that this relationship can also be obtained using a variational method based on the principle ofIeast action.