Reply to "Comment on 'Guided electromagnetic waves propagating in a plane dielectric waveguide with nonlinear permittivity'"

The preceding Comment contains statements that we feel are inaccurate and that lead one to think that the problem we study in Phys. Rev. A 91, 013840 (2015) was solved long ago. However, we argue that our results are new and add to the understanding of the process of transverse electric wave propagation in a Kerr medium. In our Reply we contest the critical statements that are given in the Comment.