  The non-linear flow modes, $v_{4,22}$, $v_{5,32}$ and $v_{6,33}$ as a
function of transverse momentum ($p_{\mathrm{T}}$) have been measured for the
first time in Pb--Pb collisions at $\sqrt{s_{\rm{NN}}} = 5.02$ TeV for
identified particles, i.e. charged pions, kaons and (anti-)protons. These
observables probe the contribution of the second and third initial anisotropy
coefficients to the higher order flow harmonics. Interestingly, all the
characteristic features observed in previous $p_{\mathrm{T}}$-differential as
well as $p_{\mathrm{T}}$-integrated measurements (e.g. $v_{2}$ and $v_{3}$) for
various particle species are present in these measurements, i.e. increase of
magnitude with increasing centrality percentile, a mass ordering in the low
$p_{\mathrm{T}}$ region and a particle type grouping in the intermediate
$p_{\mathrm{T}}$ region. The results cover 0--1\% (ultra-central collisions),
10--20\% (mid-central collisions) and 40--50\% (mid-peripheral collisions)
centrality intervals and allow to test models that attempt to describe initial
conditions and the mode-coupling of different harmonics.
