Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization

Bacui Li; Fuzhang Wang; Sohail Nadeem

doi:10.1371/journal.pone.0303982

Peer Review History

Original SubmissionJanuary 18, 2024
9 Feb 2024 Decision Letter - Tao Peng, Editor PONE-D-24-02488Explicit and exact travelling wave solutions for Hirota equation and Computerized MechanizationPLOS ONE Dear Dr. Wang, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Mar 25 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. Thank you for stating the following in the Acknowledgments Section of your manuscript: "The work was supported by the Natural Science Foundation of Jiangxi Province (Project No. 20224BAB201018)." We note that you have provided additional information within the Acknowledgements Section that is not currently declared in your Funding Statement. Please note that funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form. Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. 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In addition, the authors should complete this rebuttal process within the rebuttal deadline, and if you need more time for this rebuttal process on the reasonable request, please contact us. Submission with both clean version and highlight version of the revised manuscript is recommended, which can help Editor board to make the quick decision, but not a mandatory requirement. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: Yes ****** 4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes ****** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: In the study, innovative methods were used to derive new solutions for the Hirota equation, crucial for modeling nonlinear phenomena. The findings include solitary wave and Jacobian elliptic function solutions. The approach, applicable to other nonlinear PDEs, emphasizes the potential for broader implications in mathematics and physics. Further exploration and application of these methods could yield significant advancements in understanding complex systems. I would suggest accepting it after the following major concerns are addressed: 1. In the introduction part, integrating a brief overview of the methods' novelty compared to traditional approaches can captivate the reader's interest and underscore the study's significance in the broader field of nonlinear optics. 2. Add the limitations of the study in the conclusion part. Discussing potential applications or implications in practical scenarios would bridge the gap between theoretical solutions and real-world relevance. 3. In "Introduction of the extended hyperbolic auxiliary equation method" part, to improve this section, consider incorporating a more detailed explanation of the physical significance and applicability of each case scenario. 4. To enhance "Solutions of the elliptic-like equation" section, incorporating a clear, concise summary of each solution's physical interpretation could be beneficial. Visual representations or graphs of the solutions could aid in comprehensibility. 5. Improving the article's structure: could involve organizing content into clearly defined sections. Reviewer #2: Review for PONE-D-24-02488 The research work focuses on finding explicit and exact travelling wave solutions for the Hirota equation through various mathematical methods. The paper presents a significant contribution by introducing new solutions for the Hirota equation, enhancing the understanding of nonlinear physical phenomena. Here are some suggestions for this article: 1. How do the chosen methods (power-exponential function method and the extended hyperbolic auxiliary equation method) compare in efficiency and accuracy with other contemporary approaches to solving the Hirota equation? 2. Can the authors elaborate on the unique aspects of the solutions found for the Hirota equation and how these contribute to advancing the field? 3. What are the theoretical implications of the new solutions for understanding complex systems modeled by the Hirota equation? 4. Are there specific practical applications in physics or engineering where the new solutions could be particularly beneficial? How do these solutions improve upon existing models or methodologies in practical scenarios? 5. What are the limitations of the current study, and what assumptions have been made in the application of the methods? How do these limitations affect the interpretation of the results? 6. Based on the findings, what future research directions do the authors suggest? Are there any particular areas within the field where these solutions could open up new lines of inquiry? 7. Could the authors provide more detail on the data or simulations used to verify the solutions, ensuring reproducibility for other researchers? 8. How do the solutions derived in this study perform in comparison to existing solutions to the Hirota equation in terms of stability, solvability, and physical relevance? Overall, the paper makes contributions to the field of nonlinear partial differential equations, particularly in the study of the Hirota equation. Expanding on certain aspects as suggested could make the paper even more robust and impactful. ****** 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: Yes: Taolin Qin Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. Attachments Attachment Submitted filename: Comments on PONE-D-24-02488.pdf https://doi.org/10.1371/journal.pone.0303982.r001
Revision 1
13 Mar 2024 Author Response We highly appreciate your detailed and helpful comments on our manuscript, which have helped to significantly improve academic quality and readability of this paper. The revised version has considered all of your recommendations and criticisms. Reply to reviewer 1: 1. In the introduction part, integrating a brief overview of the methods' novelty compared to traditional approaches can captivate the reader's interest and underscore the study's significance in the broader field of nonlinear optics. We have added a brief overview of the current method and traditional method. In short, the key idea of the traditional auxiliary equation method is to use the solutions of new first-order nonlinear ordinary differential equation instead of tanh(.) in tanh-function method and extended tanh-function method. By using the extended hyperbolic auxiliary equation method, a series of new travelling wave solutions have been obtained including not only Jacobian elliptic function solutions but also solitary wave solutions and trigonometric function solutions. 2. Add the limitations of the study in the conclusion part. Discussing potential applications or implications in practical scenarios would bridge the gap between theoretical solutions and real-world relevance. According to your suggestion, we have added the limitations of the study in the conclusion part. In short, the limitations of the study lie in that the method is only used for integer-order equations, potential applications to fractional derivative equations will be also interesting for practical problems. 3. In "Introduction of the extended hyperbolic auxiliary equation method" part, to improve this section, consider incorporating a more detailed explanation of the physical significance and applicability of each case scenario. According to your suggestion, we have provided a more detailed explanation of the physical significance and applicability of each case scenario in "Introduction of the extended hyperbolic auxiliary equation method" part. 4. To enhance "Solutions of the elliptic-like equation" section, incorporating a clear, concise summary of each solution's physical interpretation could be beneficial. Visual representations or graphs of the solutions could aid in comprehensibility. According to your suggestion, we have provided a clear and concise summary of the physical explanations for each solution in "Solutions of the elliptic-like equation" section. In addition, we have drawn some pictures and added corresponding description. 5. Improving the article's structure: could involve organizing content into clearly defined sections. According to your suggestion, we have re-organized Section 2 into clearly defined sub-sections to improve the article's structure. Reply to reviewer 2: 1.How do the chosen methods (power-exponential function method and the extended hyperbolic auxiliary equation method) compare in efficiency and accuracy with other contemporary approaches to solving the Hirota equation? In this paper, we have investigated the explicit and exact travelling wave solutions of the Hirota equation. Compared to the traditional auxiliary equation method, a series of new travelling wave solutions have been obtained by using the extended hyperbolic auxiliary equation method which include not only Jacobian elliptic function solutions but also solitary wave solutions and trigonometric function solutions. 2.Can the authors elaborate on the unique aspects of the solutions found for the Hirota equation and how these contribute to advancing the field? The Hirota equation is a very important PDE, which is commonly used to describe the mathematical model of optical soliton propagation in dispersive optical fibers from the field of nonlinear optics. The solutions obtained in the paper are useful for further understanding the propagation of optical fibers in nonlinear optical fibers. Moreover, the results of this article can also make up for the lack of qualitative analysis of Hirota equation and its perturbation system. 3.What are the theoretical implications of the new solutions for understanding complex systems modeled by the Hirota equation? Exact solutions extracted from Hirota equation are known to provide complete information on real-world occurrences. These solutions obtained in this manuscript are believed to play a role in understanding the dynamical aspects of the Hirota equation. 4.Are there specific practical applications in physics or engineering where the new solutions could be particularly beneficial? How do these solutions improve upon existing models or methodologies in practical scenarios? Your question is very interesting. The main goal of our manuscript is to we present the explicit solutions of the subsidiary elliptic-like equation. With the aid of the subsidiary elliptic-like equation and a simple transformation, we can derive the exact solutions of Hirota equation. The practical application in physics or engineering beyond the scope of our research, we will consider it as our future investigation. 5.What are the limitations of the current study, and what assumptions have been made in the application of the methods? How do these limitations affect the interpretation of the results? According to your suggestion, we have added the limitations of the study in the conclusion part. In short, the limitations of the study lie in that the method is only used for integer-order equations. 6.Based on the findings, what future research directions do the authors suggest? Are there any particular areas within the field where these solutions could open up new lines of inquiry? In the conclusion part, we have added potential research directions which include the applications to fractional derivative equations. There is a wide range of applications, part of which is being under investigation by the authors recently. 7.Could the authors provide more detail on the data or simulations used to verify the solutions, ensuring reproducibility for other researchers? To ensure reproducibility for other researchers, we have tried our best to make the whole manuscript clear-to-understand. Researchers who are interested in our work can reproduce our result easily with the help of MAPLE. 8.How do the solutions derived in this study perform in comparison to existing solutions to the Hirota equation in terms of stability, solvability, and physical relevance? Compared with the traditional auxiliary equation method, a series of new travelling wave solutions have been obtained by using the extended hyperbolic auxiliary equation method which include the Jacobian elliptic function solutions, solitary wave solutions and trigonometric function solutions. https://doi.org/10.1371/journal.pone.0303982.r002
29 Apr 2024 Decision Letter - Tao Peng, Editor PONE-D-24-02488R1Explicit and exact travelling wave solutions for Hirota equation and Computerized MechanizationPLOS ONE Dear Dr. Wang, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Jun 13 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. 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Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Additional Editor Comments: Based on the careful revision, this work could be considered to be accepted after the minor revision, where it still contains several issues, 1) language should be polished by the English native speaker, 2) image and math equations should be polished. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: All comments have been addressed Reviewer #2: All comments have been addressed ******** 2. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: Yes ****** 5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: I really appreciate you solving all the suggestions I provided and work you have done. 1. Check the image quality and format to make sure it satisfy the requirement of the Journal. Use image editing software to check and adjust the resolution. 2. Mention possible interdisciplinary collaborations that could enhance the depth and breadth of subsequent studies. 3. Discuss articles which used similar or relevant solutions to yours. Explicitly highlight the novelty and significance of the new solutions to strengthen your claim. Consider stating more clearly how these solutions differ from those found in previous works and why they are relevant. Reviewer #2: (No Response) ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: Yes: Taolin Qin Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0303982.r003
Revision 2
1 May 2024 Author Response We highly appreciate your detailed and helpful comments on our manuscript, which have helped to significantly improve academic quality and readability of this paper. The revised version has considered all of your recommendations and criticisms. Reply to reviewer 1: 1. Check the image quality and format to make sure it satisfies the requirement of the Journal. Use image editing software to check and adjust the resolution. We have checked the image quality and changed the format under the requirement of the journal. 2. Mention possible interdisciplinary collaborations that could enhance the depth and breadth of subsequent studies. We have added the subsequent studies in the conclusions, i.e., it is also the limitations of the current manuscript. 3. Discuss articles which used similar or relevant solutions to yours. Explicitly highlight the novelty and significance of the new solutions to strengthen your claim. Consider stating more clearly how these solutions differ from those found in previous works and why they are relevant. According to your suggestion, we have revised it as far as we can. https://doi.org/10.1371/journal.pone.0303982.r004
6 May 2024 Decision Letter - Tao Peng, Editor Explicit and exact travelling wave solutions for Hirota equation and Computerized Mechanization PONE-D-24-02488R2 Dear Dr. Wang, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. If you have any questions relating to publication charges, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Tao Peng Academic Editor PLOS ONE Additional Editor Comments (optional): Reviewers' comments: https://doi.org/10.1371/journal.pone.0303982.r005
Formally Accepted
9 May 2024 Acceptance Letter - Tao Peng, Editor PONE-D-24-02488R2 PLOS ONE Dear Dr. Wang, I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now being handed over to our production team. At this stage, our production department will prepare your paper for publication. This includes ensuring the following: * All references, tables, and figures are properly cited * All relevant supporting information is included in the manuscript submission, * There are no issues that prevent the paper from being properly typeset If revisions are needed, the production department will contact you directly to resolve them. If no revisions are needed, you will receive an email when the publication date has been set. At this time, we do not offer pre-publication proofs to authors during production of the accepted work. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few weeks to review your paper and let you know the next and final steps. Lastly, if your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. If we can help with anything else, please email us at customercare@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Tao Peng Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0303982.r006

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