  We study a coevolving nonlinear voter model describing the coupled evolution
of the states of the nodes and the network topology. Nonlinearity of the
interaction is measured by a parameter q. The network topology changes by
rewiring links at a rate p. By analytical and numerical analysis we obtain a
phase diagram in p, q parameter space with three different phases: Dynamically
active coexistence phase in a single component network, absorbing consensus
phase in a single component network, and absorbing phase in a fragmented
network. For finite systems the active phase has a lifetime that grows
exponentially with system size, at variance with the similar phase for the
linear voter model that has a lifetime proportional to system size. We find
three transition lines that meet at the point of the fragmentation transition
of the linear voter model. A first transition line corresponds to a continuous
absorbing transition between the active and fragmented phases. The other two
transition lines are discontinuous transitions fundamentally different from the
transition of the linear voter model. One is a fragmentation transition between
the consensus and fragmented phases, and the other is an absorbing transition
in a single component network between the active and consensus phases.
