  A weak formulation is devised for the K(m,n) equation which is a nonlinearly
dispersive generalization of the gKdV equation having compacton solutions. With
this formulation, explicit weak compacton solutions are derived, including ones
that do not exist as classical (strong) solutions. Similar results are obtained
for a nonlinearly dispersive generalization of the gKP equation in two
dimensions, which possesses line compacton solutions.
