  We numerically model the evolution of a pair of coherently split
quasicondensates. A truly one-dimensional case is assumed, so that the loss of
the (initially high) coherence between the two quasicondensates is due to
dephasing only, but not due to the violation of integrability and subsequent
thermalization (which are excluded from the present model). We confirm the
subexponential time evolution of the coherence between two quasicondensates
$\propto \exp [-(t/t_0)^{2/3}]$, experimentally observed by S. Hofferberth {\em
et. al.}, Nature {\bf 449}, 324 (2007). The characteristic time $t_0$ is found
to scale as the square of the ratio of the linear density of a quasicondensate
to its temperature, and we analyze the full distribution function of the
interference contrast and the decay of the phase correlation.
