Optical Solitons and Conservation Laws for the Concatenation Model: Undetermined Coefficients and Multipliers Approach
, Luminita Moraru 11,* and Puiu Lucian Georgescu 11Round 1
Reviewer 1 Report
Congrats on the nice work. I have two minor comments,
line 72: define --> defined above
line 87: determine --> determined
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Journal: Universe (Section: Mathematical Physics; Special Issue: Research on Optical Soliton Perturbation)
Manuscript ID: universe-2047266
Type of manuscript: Article
Title: Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach
Authors: Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. Gonzalez-Gaxiola, Luminita Moraru, Puiu Lucian Georgescu
Reviewer invited: November 12, 2022
Report submitted: November 12, 2022
The manuscript universe-2047266 “Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach” by Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. Gonzalez-Gaxiola, Luminita Moraru, and Puiu Lucian Georgescu deals with soliton solutions of some rather complicated differential equation with partial derivatives.
The manuscript is organized as follows. In Section 1, the Authors give a brief introduction. This section also contains Subsection 1.1, which introduces the main equation that will be solved. Section 2 presents construction of bright soliton and dark soliton solutions, as well as singular solutions of two types. In Section 3, the conservation laws are briefly discussed. Finally, Section 4 presents some brief discussion and concluding remarks. The list of references contains 15 items and is somewhat adequate.
The results presented in the manuscript are new (at least I am not familiar with similar results). In general, optical solitons, as well as topological solitons, are important for many applications in physics, we see a large number of publications related to this topic. Nevertheless, I have several comments and suggestions about this manuscript:
1. In the Introduction, it is written “Painleve analysis for this model has been carried out very recently by Kudryashov et. al. [6]”. In this context, more recent (e.g., 2020-2022) publications of Prof. N.A.Kudryashov on Painleve analysis should be cited in addition to Refs. [6,7].
2. “Universe” is a pretty much a physical journal, hence in the Introduction it is necessary to pay more attention to possible physical contexts, in which equation (1) can appear. The appropriate citation should be added too.
3. It the Introduction, it is written “This emerged into an ocean of novel concepts that is consistently being studied and analyzed [1–15]”. After this phrase, the so-called topological solitons should be mentioned, because it is very wide class of solutions of non-linear Klein-Gordon equations. I suggest to cite in this context the following book: N. Manton and P. Sutcliffe, “Topological Solitons”, Cambridge University Press, Cambridge U.K. (2004), see https://doi.org/10.1017/CBO9780511617034. Also, several very recent papers should be mentioned:
https://doi.org/10.1016/j.chaos.2022.112805
https://doi.org/10.1142/S0217979222500424
https://doi.org/10.1142/S0217979222501429
https://doi.org/10.1016/j.aop.2021.168739
4. Surname of the third author of Ref. [7] is incorrect. The correct is “Borodina”.
I would like the Authors to accurately answer each point. If the Authors agree with the point, I ask them to amend the text of the manuscript accordingly. In all cases when the Authors do not agree with my suggestion, I kindly ask them to give a reasoned answer.
The manuscript universe-2047266 in its current form cannot be recommended for publication in Universe, I recommend some adequate revision. After the Authors address all my questions and suggestions, I will be happy to review the revised version of the manuscript.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
The authors mainly investigated a LPD equation and SS equation, they derived some soliton solutions via the analytical method. As the two models are very important in many nonlinear fields, the solutions are very valuable. So I recommend this artical can be published.
Supplementary comments
The main question addressed by the research is to derive some exact soliton solutions for a very important nonlinear model.
I think this manuscript is original, the model in this manuscript has many physical meanings, they derived some exact solutions which have many values in mathematics and physics. The conclusions are consistent with evidence and arguments.
Compared other published, this manuscript derived some new and novel soliton solutions via different method. So not only the solutions are new and novel, but also the methods have benefits in mathematics.
I suggest the authors to simulate the solutions by some numerical methods.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Journal: Universe (Section: Mathematical Physics; Special Issue: Research on Optical Soliton Perturbation)
Manuscript ID: universe-2047266 (revised version)
Type of manuscript: Article
Title: Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach
Authors: Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. Gonzalez-Gaxiola, Luminita Moraru, Puiu Lucian Georgescu
Reviewer invited: November 28, 2022
Report submitted: November 29, 2022
The revised version of the manuscript universe-2047266 “Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach” by Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. Gonzalez-Gaxiola, Luminita Moraru, and Puiu Lucian Georgescu deals with soliton solutions of some rather complicated differential equation with partial derivatives.
After revision, the overall structure of the manuscript remains unchanged: in Section 1, the Authors give a brief introduction, this section also contains Subsection 1.1, which introduces the main equation that will be solved; Section 2 presents construction of bright soliton and dark soliton solutions, as well as singular solutions of two types; in Section 3, the conservation laws are briefly discussed; finally, Section 4 presents some brief discussion and concluding remarks; the list of references now contains 25 items and is quite adequate.
As I have already mentioned in the previous report, the results presented in the manuscript are new and could be interesting to scientific community because optical solitons, as well as topological solitons, are important for many applications in physics.
The Authors have revised the manuscript thereby substantially improving the presentation of the results. In particular, citations of recent papers on Painleve analysis and topological solitons have been added, a new paragraph about physical applications is written, figures have been added, a typo in surname of the third author of Ref. [6] is corrected.
Summarizing the above, I think that current version of universe-2047266 “Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach” by Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. Gonzalez-Gaxiola, Luminita Moraru, and Puiu Lucian Georgescu can be published in “Universe”.
