Qualitative Analysis and Traveling Wave Solutions of a (3 + 1)- Dimensional Generalized Nonlinear Konopelchenko-Dubrovsky-Kaup-Kupershmidt System
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsIn this paper, the authors carried out a qualitative analysis of the traveling wave solutions of the generalized nonlinear fractional Konopelchenko-Dubrovsky-Kaup- Kupershmidt system of equations.
The traveling wave solution of fractional Konopelchenko-Dubrovsky-Kaup- Kupershmidt system is studied based on the complete discriminant system method, and its three-dimensional, two-dimensional graphs and contour plots are plotted.
A revision is needed to improve the paper’s quality.
Observations:
1). After equation (1), in line 49 the authors gave the name of the fractional operator used. In my opinion, the information is insufficient. Not all readers are familiar with the conformable fractional derivative operator. The authors should provide a summary of the theory related to this differential operator and present some of its properties.
Only in this way can the derivation of equation (3) be understood.
2). Verify and correct the second equation in (9). The form in manuscript is incorrect.
The same problem is for the equation (12).
3). The authors should provide an example comparing the result from the fractional case with the one corresponding to the case alpa = 1. In this way, they could highlight the advantages/disadvantages of the fractional model.
4). Also, the authors should explain whether the conformable fractional derivative is a proper fractional derivative or reduces to the derivative of integer order alpha=1.
In this direction, I suggest the article: https://doi.org/10.1016/j.cnsns.2015.06.007.
Author Response
1). After equation (1), in line 49 the authors gave the name of the fractional operator used. In my opinion, the information is insufficient. Not all readers are familiar with the conformable fractional derivative operator. The authors should provide a summary of the theory related to this differential operator and present some of its properties.
Only in this way can the derivation of equation (3) be understood.
Response 1: Thank you for the reviewer's suggestion. In the revised manuscript, we will provide the definition and corresponding properties of its derivative.
2). Verify and correct the second equation in (9). The form in manuscript is incorrect.
The same problem is for the equation (12).
Response 2: Thank you. There is indeed an error. We have already made modifications.
3). The authors should provide an example comparing the result from the fractional case with the one corresponding to the case alpa = 1. In this way, they could highlight the advantages/disadvantages of the fractional model.
Response 3: Thank you for the reviewer's suggestions. We will add this section in both the first and fifth sections.
4). Also, the authors should explain whether the conformable fractional derivative is a proper fractional derivative or reduces to the derivative of integer order alpha=1.
In this direction, I suggest the article: https://doi.org/10.1016/j.cnsns.2015.06.007.
Response 4: Thank you for your constructive feedback. We will revise the paper based on the literature provided by the reviewer.
Reviewer 2 Report
Comments and Suggestions for AuthorsPlease see the attachment file.
Comments for author File: 
Comments.pdf
Author Response
- In line 57, The qualitative · · should be the qualitative · · ·
Response 1: Thank you for the reviewer's suggestions. We have corrected the grammar error.
- In equation (11), −(2aiUi + a1) should be −(2a2Ui + a1)
Response 2: Thank you for the reviewer's suggestions. We will correct the error.
- In line 113, Professor Liu [22] should be Liu [22]
Response 3: Thank you for the reviewer's suggestions. We have removed unnecessary words.
- In line 134, given should be give
Response 4: Thank you for the reviewer's suggestions. We have corrected the grammar error.
Thank you very much for your constructive comments and suggestions. We have made revisions to all the issues you mentioned in the revised manuscript and highlighted the changes in blue font.
Reviewer 3 Report
Comments and Suggestions for AuthorsDear Authors,
The manuscript needs revision. My comments are presented below:
1.The Introduction does not present the detailed background of the (3+1)-dimensional generalized nonlinear fractional Konopelchenko-Dubrovsky-Kaup- Kupershmidt system (1). The authors should first reference where this equation (1) was suggested and which methods were applied before.
2.Please, present the description for r1, r2…r9 in Eq. (1)
3.Please, present the description for 𝜶 in Eq. (2)
4.Explain why a quadratic polynomial in Eq. (5) was chosen
5.It is common for researchers to use only one function, 𝐴1cos (𝑘1𝜍), in studying dynamic behavior. Explain why applying two functions (𝐴1cos(𝑘1𝜍),𝐴2sin (𝑘2𝜍)) is necessary in Eq. (12).
6.The complete discriminant system method is used in this work. Please present some references where this method was applied before.
7.Please check the solutions 𝑢4−𝑢8. Are they really one-dimensional or these typos?
8.What kind of traveling wave solutions are presented in Figs. 5, 6
Author Response
Please refer to the attachment for your response to the review comments.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsIn the revised manuscript, the authors made the requested corrections and additins.
Reviewer 3 Report
Comments and Suggestions for AuthorsDear Authors,
There are no other comments. The manuscript can be published.
