  In our previous work arXiv:1704.08675, we pointed out that various multi-cut
solutions exist in the Chern-Simons (CS) matrix models at large-$N$ due to a
curious structure of the saddle point equations. In the ABJM matrix model,
these multi-cut solutions might be regarded as the condensations of the
D2-brane instantons. However many of these multi-cut solutions including the
ones corresponding to the condensations of the D2-brane instantons were
obtained numerically only. In the current work, we propose an ansatz for the
multi-cut solutions which may allow us to derive the analytic expressions for
all these solutions. As a demonstration, we derive several novel analytic
solutions in the pure CS matrix model and the ABJM matrix model. We also
develop the argument for the connection to the instantons.
