New Abundant Analytical Solitons to the Fractional Mathematical Physics Model via Three Distinct Schemes

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Significance of model (1) should be addressed. 

2. For all density 2D plots, mention the axes representation. 

3. More interpretation needed for ALL figures.

4. Authors claimed different dynamics for some parameters. Kindly, discuss the impact of parameters on soliton dynamics.

5. Authors have not cited papers in the year of 2024 which are very recent and updated. Kindly add recent references.

Comments on the Quality of English Language

Quality of English is Ok

Author Response

Responses to Reviwers Comments

Journal Name:  Mathematics

Manuscript ID: mathematics-3313312

 

Paper Entitled: New abundant analytical solitons to the fractional mathematical

physics model via three distinct schemes

 

We authors are very thankful to the reviewers for the suggestions to make the manuscript more reliable and suitable for publication. All queries are entertained in the revised manuscript and highlighted with Green paint.

                                 

                                  Reviewer 1: Comments and our responses

Comment 1:	Significance of model (1) should be addressed.
Response:	Dear, we added the significance of model (1).
Comment 2:	For all density 2D plots, mention the axes representation.
Response:	Dear, we done.
Comment 3:	More interpretation needed for ALL figures.
Response:	Dear, we added more interpretation for all figures.
Comment 4:	Authors claimed different dynamics for some parameters. Kindly, discuss the impact   of parameters on soliton dynamics.
Response:	Dear, we mentioned that dynamical behavior of some obtained solutions and we have done this through two-dimensional, three-dimensional and contour graphs.
Comment 5:	Authors have not cited papers in the year of 2024 which are very recent and updated. Kindly add recent references.
Response:	Dear, we added.

                

Finally: We authors are again thankful to you for your valuable comments.

 We appreciate the referees for spending time and taking care of our manuscript.

Thank you for your useful comments and suggestions on the structure of our manuscript.

The revised version of our manuscript has been submitted to your journal.

We look forward to your positive response.

Best wishes.

Prof. Ahmet Bekir

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

 

In the present paper the author investigated new abundant analytical solitons to the fractional mathematical physics model via three distinct schemes.

 

In this manuscript, the authors have derived new types of truncated M-fractional wave solitons to the mathematical physics model; simplified Modified Camassa-Holm model. By utilizing the simplest equation, the Sardar sub-equation, and the generalized Kudryashov schemes, the required solutions are obtained . The obtained results consisting on the dark, singular, periodic, dark-bright, and many other analytical solitons. Furthermore, dynamical behaviors of some obtained solutions are represented by two-dimensional (2D), three-dimensional(3D), and Contour graphs. An effect of fractional derivative is shown graphically.

 

This manuscript is scientifically sounds good, actual and important to the field. Its contents are interesting and helpful for wide audience.  However, some  revisions are needed.

(1)There are too many formulas and lack of verbal description. The authors should add some language description to connect these formulas. For example, in subsection 4.1, the reason for the classification is unclear.

(2)The formatting of the formula needs further adjustment, such as formula (106) - (121).

(3)The authors should add some descriptions of the images to explain the different characteristics and physical meanings of the obtained solutions.

(4) In the section of introduction, the description soliton theory and methods are not comprehensive enough. There are many efficient methods that have been verified to be very effective. For example,

Wang et al. (J. Math. Phys. 2021, 62, 093510) successfully deduced the three-component coupled Hirota hierarchy via employing the dressing method.  In addition, by using Riemann-Hilbert method, Li and Tian (Stud. Appl. Math. 2022, 148, 577–605) solved the Cauchy problem of the general n-component nonlinear Schrödinger equations, and gave the N-soliton solutions. Besides, a conjecture about the law of nonlinear wave propagation was proposed. Moreover,  with respect to deriving the solutions of Wadati-Konno-Ichikawa equation and complex short pulse equation, Li, Tian, Yang and Fan have done some interesting work by employing the Dbar-steepest descent method. They solved the long-time asymptotic behavior of the solutions of these equations, and proved the soliton resolution conjecture and the asymptotic stability of solutions of these equations.(Adv. Math.，409 (2022) 108639; 

 

Authors should carefully discuss these questions. I recommend the manuscript to be published after the modification.

 

 

Author Response

Responses to Reviewers Comments

Journal Name:  Mathematics

Manuscript ID: mathematics-3313312

Paper Entitled: New abundant analytical solitons to the fractional mathematical

physics model via three distinct schemes

We authors are very thankful to the reviewers for the suggestions to make the manuscript more reliable and suitable for publication. All queries are entertained in the revised manuscript and highlighted with Green paint.

                                 

                                  Reviewer 2: Comments and our responses

Comment 1:	There are too many formulas and lack of verbal description. The authors should add some language description to connect these formulas. For example, in subsection 4.1, the reason for the classification is unclear.
Response:	Dear, we done.
Comment 2:	The formatting of the formula needs further adjustment, such as formula (106) - (121).
Response:	Dear, we done.
Comment 3:	The authors should add some descriptions of the images to explain the different characteristics and physical meanings of the obtained solutions.
Response:	Dear, we done.
Comment 4:	In the section of introduction, the description soliton theory and methods are not comprehensive enough. There are many efficient methods that have been verified to be very effective. For example, Wang et al. (J. Math. Phys. 2021, 62, 093510) successfully deduced the three-component coupled Hirota hierarchy via employing the dressing method.  In addition, by using Riemann-Hilbert method, Li and Tian (Stud. Appl. Math. 2022, 148, 577–605) solved the Cauchy problem of the general n-component nonlinear Schrödinger equations, and gave the N-soliton solutions. Besides, a conjecture about the law of nonlinear wave propagation was proposed. Moreover,  with respect to deriving the solutions of Wadati-Konno-Ichikawa equation and complex short pulse equation, Li, Tian, Yang and Fan have done some interesting work by employing the Dbar-steepest descent method. They solved the long-time asymptotic behavior of the solutions of these equations, and proved the soliton resolution conjecture and the asymptotic stability of solutions of these equations.(Adv. Math.，409 (2022) 108639;
Response:	Dear, we modified the introduction section.

Finally: We authors are again thankful to you for your valuable comments.

 We appreciate the referees for spending time and taking care of our manuscript.

Thank you for your useful comments and suggestions on the structure of our manuscript.

The revised version of our manuscript has been submitted to your journal.

We look forward to your positive response.

Best wishes.

Prof. Ahmet Bekir

Author Response File: Author Response.pdf