Correction to: An analytical comprehensive solution for the superficial waves appearing in gravity-driven flows of liquid films

1 Correction to: Z. Angew. Math. Phys. (2020) 71:122 https://doi.org/10.1007/s00033-020-01349-x

In the original publication of the article, Eq. (23) was incorrectly published. The correct version is given below:

$$\begin{aligned}&i\alpha Re[(c - \overline{U})D + D\overline{U}]\tilde{\Psi } - 4\alpha ^{2}\overline{\eta }D \tilde{\Psi }\nonumber \\&\quad + (D^{2}+\alpha ^{2})\bigg [D\overline{\epsilon } + \overline{\epsilon }D + i\alpha \overline{\epsilon } \bigg (\cot (\theta ) + \frac{\alpha ^{2}}{We_{m}} \bigg ) \bigg ]\tilde{\Psi } = 0 \ \ at \ \ \overline{y} = 0 \end{aligned}$$

(23)

The original article has been corrected.