We develop { \em the first analytical theory of multikinks} for strongly { \em dispersive nonlinear systems}, considering the examples of the weakly discrete sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise parabolic potential. We reveal that there are no $2\pi$-kinks for this model, but there exist { \em discrete sets} of $2\pi N$-kinks for all N>1. We also show their bifurcation structure in driven damped systems.
Categories: patt-sol nlin.PS