  We study the frustrated ferromagnetic spin-1 chains, where the ferromagnetic
nearest-neighbor coupling competes with the antiferromagnetic
next-nearest-neighbor coupling. We use the density matrix renormalization group
to obtain the ground states. Through the analysis of spin-spin correlations we
identify the double Haldane phase as well as the ferromagnetic phase. It is
shown that the ferromagnetic coupling leads to incommensurate correlations in
the double Haldane phase. Such short-range correlations transform continuously
into the ferromagnetic instability at the transition to the ferromagnetic
phase. We also compare the results with the spin-1/2 and classical spin
systems, and discuss the string orders in the system.
