  Using a time-dependent modified nonlinear Schr\"odinger equation (m-NLSE) --
where the conventional chemical potential proportional to the density is
replaced by the one inferred from Lieb-Liniger's exact solution -- we study
frequencies of the collective monopole excitations of a one-dimensional (1D)
Bose gas. We find that our method accurately reproduces the results of a recent
experimental study [E. Haller et al., Science Vol. 325, 1224 (2009)] in the
full spectrum of interaction regimes from the ideal gas, through the mean-field
regime, through the mean-field Thomas-Fermi regime, all the way to the
Tonks-Giradeau gas. While the former two are accessible by the standard
time-dependent NLSE and inaccessible by the time-dependent local density
approximation (LDA), the situation reverses in the latter case. However, the
m-NLSE treats all these regimes within a single numerical method.
