  By means of direct simulations and theoretical analysis, we study the
nonlinear propagation of truncated Airy pulses in an optical fiber exhibiting
both anomalous second-order and strong positive third-order dispersions. It is
found that the Airy pulse first reaches a finite-size focal area as determined
by the relative strength of the two dispersion terms, and then undergoes an
inversion transformation such that it continues to travel with an opposite
acceleration. The system notably features tight focusing if the third-order
dispersion is a dominant factor. These effects are partially reduced by a Kerr
nonlinearity.
