Shallow Water Waves and Conservation Laws with Dispersion Triplet

Round 1

Reviewer 1 Report

The authors consider shallow water wave equations and their exact solutions and conservation laws. The topic if of current interest to soliton scientists and the results amend the existing literature on related problems. There is a general one-to-one correspondence between a pair of a symmetry and an adjoint symmetry and a conservation law for non-Lagrangian equations. N-soliton solutions have been studied extensively as well by the Hirota bilinear method for local integrable equations and by the Riemann-Hilbert problems for nonlocal integrable equations (see, e.g., Acta Mathematica Scientia, 42(2022), 127-140; Physica D, 430(2022), 133078 and Mathematics, 10(2022), 870). The manuscript successfully presents some interesting and potentially important analyses on a class of nonlinear shallow water wave equations. I would, therefore, like to recommend publishing the manuscript as long as the authors could amend and/or revise the manuscript to discuss about those recent studies on N-soliton solutions in the literature. In this way, the manuscript will definitely attract more attention to such interesting studies from the international research community. A revised manuscript will be reconsidered and recommended for publication in the journal. 

Author Response

Dear Respected Editor,

We the authors are submitting the revised version of the manuscript numbered applsci—1662054. 

First of all, we would like to thank the Reviewers for their high quality and constructive reviews of our manuscript, and the Editor for his careful reading.

Based on the suggestions of the referee 1, we have made the following revisions:

Reviewer—1

1. The discussion on N—soliton solution is now given at the end of the first paragraph in Section—1.
2. The suggested works are also cited and they are [11—13].
3. These changes are written in green.

Please feel free to get back to us if there is anything further required. We are looking forward to hearing from you.

Thank you very much.

Reviewer 2 Report

Review Report

Manuscript No.: applsci-1662054-peer-review-v1

I would start by commending the authors for the job well done. However, this paper is not suitable enough to be published in its current form.

• The English needs to be polished, punctuation mark needs to be administered after each equation.
• The abstract is too short, and it should be extended to clarify the main motivation.
• Keywords should not include any ward existed in the title.
• The properties and some details about Eq. (1) must be added. For details about this equation, the authors must add some related references.
• The dynamical behaviors for each figure must be discussed after all figures to describe the solutions propagation.
• In section 2.2, The properties, and some details about Eq. (20) must be added. For details about this equation, the authors must add some related references.
• In section 3, The properties, and some details about Eq. (45) must be added. For details about this equation, the authors must add some related references.
• In subsection 2.1.1 some references must be added to the used method.
• Conclusion must be extended, and the future work must be added.

 

However, I would suggest that the paper should be accepted with moderate revision due to some of the corrections I pointed above and in order to raise the standard of this paper. I will be available for further revision of this paper.

 

Comments for author File: Comments.pdf

Author Response

Dear Respected Editor,

We the authors are submitting the revised version of the manuscript numbered applsci—1662054. 

First of all, we would like to thank the Reviewers for their high quality and constructive reviews of our manuscript, and the Editor for his careful reading.

Based on the suggestions of the referee 2, we have made the following revisions:

 

Reviewer—2

1. The abstract is expanded.
2. The keywords are replaced.
3. The details from equation (1) are now included along with cited references.
4. In Section 2.1, references are now given.
5. In equation (20), references and the details of the equation are given.
6. In equation (45), the details and the references are given.
7. The conclusions section is now expanded and future work is also included which is located in the second paragraph.
8. The English language is polished with special attention to punctuation.
9. The figure captions talked about the solitary wave with no radiation components.
10. These changes are written in blue.

Please feel free to get back to us if there is anything further required. We are looking forward to hearing from you.

Thank you very much.