  We present a new approach for search of coexisting classes of localised modes
admitted by the repulsive (defocusing) scalar or vector nonlinear
Schr\"odinger-type equations. The approach is based on the observation that
generic solutions of the corresponding stationary system have singularities at
finite points on the real axis. We start with establishing conditions on the
initial data of the associated Cauchy problem that guarantee the formation of a
singularity. Making use of these sufficient conditions, we identify the
bounded, nonsingular, solutions --- and then classify them according to their
asymptotic behaviour. To determine the bounded solutions, a properly chosen
space of initial data is scanned numerically. Due to asymptotic or symmetry
considerations, we can limit ourselves to a one- or two-dimensional space. For
each set of initial conditions we compute the distances $X^{\pm}$ to the
nearest forward and backward singularities; large $X^+$ or $X^-$ indicate the
proximity to a bounded solution. We illustrate our method with the
Gross-Pitaevskii equation with a $\PT$-symmetric complex potential, a system of
coupled Gross-Pitaevskii equations with real potentials, and the
Lugiato-Lefever equation with normal dispersion.
