  We theoretically and numerically investigate the evolution of discrete
soliton in a 1D linearly chirped nonlinear waveguide array (WA). The discrete
soliton is self-accelerated inside the transversely chirped WA and emits a
\textit{dynamic diffractive resonant radiation} (DifRR). The radiation appears
when soliton wave-number matched with linear radiation wave. Unlike uniform WA,
the DifRR can be excited even for zero wave-number of input soliton when the
waveguide channels are chirped. The transverse modulation due to chirp
conceptually imposes a linear potential which acts as a perturbation to soliton
dynamics and leads to a monotonous wave-number shift of the propagating wave.
Exploiting perturbative variational analysis we determine the equation of
motion of soliton wave-number and use it to establish a modified phase-matching
condition which takes into account the soliton wave-number shift and
efficiently predicts the dynamic DifRR. A startling effect like generation of
dual DifRR occurs as a result of the interplay between self-accelerated soliton
and its initial wave-number. We exploit the modified phase matching relation to
understand this unique phenomenon of dual radiation and find a satisfactory
agreement with numerical result in radiation wave-number calculation.
