  We propose a higher-order Skyrme model with derivative terms of eighth, tenth
and twelfth order. Our construction yields simple and easy-to-interpret
higher-order Lagrangians. We first show that a Skyrmion with higher-order terms
proposed by Marleau has an instability in the form of a baby-Skyrmion string,
while the static energies of our construction are positive definite, implying
stability against time-independent perturbations. However, we also find that
the Hamiltonians of our construction possess two kinds of dynamical
instabilities, which may indicate the instability with respect to
time-dependent perturbations. Different from the well-known Ostrogradsky
instability, the instabilities that we find are intrinsically of nonlinear
nature and also due to the fact that even powers of the inverse metric gives a
ghost-like higher-order kinetic-like term. The vacuum state is, however,
stable. Finally, we show that at sufficiently low energies, our Hamiltonians in
the simplest cases, are stable against time-dependent perturbations.
