  We present a solution for the observed core fragmentation of filaments in the
Taurus L1517 dark cloud which previously could not be explained (Hacar et. al
2011). Core fragmentation is a vital step for the formation of stars.
Observations suggest a connection to the filamentary structure of the cloud gas
but it remains unclear which process is responsible. We show that the
gravitational instability process of an isothermal cylinder can account for the
exhibited fragmentation under the assumption that the perturbation grows on the
dominant wavelength. We use numerical simulations with the code RAMSES,
estimate observed column densities and line-of-sight velocities and compare
them to the observations. A critical factor for the observed fragmentation is
that cores grow by redistributing mass within the filament and thus the density
between the cores decreases over the fragmentation process. This often leads to
wrong dominant wavelength estimates as it is strongly dependent on the initial
central density. We argue that non-linear effects also play an important role
on the evolution of the fragmentation. Once the density perturbation grows
above the critical line-mass, non-linearity leads to an enhancement of the
central core density in comparison to the analytical prediction. Choosing the
correct initial conditions with perturbation strengths of around 20\%, leads to
inclination corrected line-of-sight velocities and central core densities
within the observational measurement error in a realistic evolution time.
