Review Manuscript ID: symmetry-1151647 Type of manuscript: Article Title: Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime modified Korteweg-de Vries hierarchies Authors: Liming Ling, Wen-Xiu Ma* Submitted to the section: Mathematics and Symmetry, Nonlocal Partial Differential Equations, Methods and Applications Date: 9 March 2021

The manuscript describes the inverse scattering aspect for the mKdV equation. It is well-written and should be recommended for publication. Here are some remarks.

• You may now transfer the typeset into the MDPI LaTeX template as the recommendation for this article is going to be positive.

• Five affiliations for one of the authors are too many and suspicious. Even some Nobel prize winners only hold one or two affiliations at one time.

• The keyword mentioned parity-time symmetry, but it was not discussed in the text.

• The citation should be written as follows: [2-7] and [10-14].

• The size of the matrices on pages 2 and 3 is not specified. The readers interpret it as 2 x 2. However, after going to Section 2, it becomes n x n. What is even more confusing, on page 6, the matrix operator \Psi has the size of (2n) x (2n). Please clarify this matter.

• On page 21, the authors re-discovered one-soliton solution for the mKdV equation. I am sure that this solution is already available in the literature. So, what is then the contribution of this paper apart from a different, rather detour approach in recovering the soliton solutions? Furthermore, the authors mentioned N-soliton solutions of the mKdV equation, but these solutions are not stated and expressed explicitly. Is that any reason for that?

• On page 20, the phrase "as normal" seems weird. Please reword it.