Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and IF 0.7 Q2 MATHEMATICS Muenster Journal of Mathematics Pub Date : 2023-08-09 DOI:10.1155/2023/7063620 Khalid K. Ali, M. Alotaibi, Mohamed Nazih Omri, M. Mehanna, A. Abdel‐Aty 求助PDF {"title":"Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mro","authors":"Khalid K. Ali, M. Alotaibi, Mohamed Nazih Omri, M. Mehanna, A. Abdel‐Aty","doi":"10.1155/2023/7063620","DOIUrl":null,"url":null,"abstract":"The fifth-order nonlinear wave equation contains terms involving higher-order spatial derivatives, such as \n \n \n \n u\n \n \n x\n x\n x\n \n \n \n and \n \n \n \n u\n \n \n x\n x\n x\n x\n x\n \n \n \n . These terms are responsible for dispersion, which affects the shape and propagation of the wave. The study of dispersion is important in many areas, including seismology, acoustics, and communication theory. In the current work, three potent analytical techniques are proposed in order to solve the fifth-order nonlinear wave equation. The used approaches are the modified auxiliary equation method, the Bernoulli Sub-ODE method, and the \n \n \n \n \n G\n \n \n ′\n \n /\n G\n \n \n \n -expansion method (MAE). Some graphs are plotted to display our findings. The solutions to the nonlinear wave equation are used to describe the nonlinear dynamics of waves in physical systems. The results show how the dynamics of the wave solutions are influenced by the system parameters, which can be used as system controllers. The new approaches used in this work helped to find new solutions for traveling waves. This could be seen as a new contribution to the field. Water waves, plasma waves, and acoustic wave behavior can be described by the obtained solutions.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Muenster Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/7063620","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0} 引用次数: 0 引用 批量引用 Abstract The fifth-order nonlinear wave equation contains terms involving higher-order spatial derivatives, such as u x x x and u x x x x x . These terms are responsible for dispersion, which affects the shape and propagation of the wave. The study of dispersion is important in many areas, including seismology, acoustics, and communication theory. In the current work, three potent analytical techniques are proposed in order to solve the fifth-order nonlinear wave equation. The used approaches are the modified auxiliary equation method, the Bernoulli Sub-ODE method, and the G ′ / G -expansion method (MAE). Some graphs are plotted to display our findings. The solutions to the nonlinear wave equation are used to describe the nonlinear dynamics of waves in physical systems. The results show how the dynamics of the wave solutions are influenced by the system parameters, which can be used as system controllers. The new approaches used in this work helped to find new solutions for traveling waves. This could be seen as a new contribution to the field. Water waves, plasma waves, and acoustic wave behavior can be described by the obtained solutions. 分享 查看原文 本刊更多论文 用Bernoulli Sub-ODE、修正辅助方程和 五阶非线性波动方程包含涉及高阶空间导数的项，如u x x x和u x x x x x x。这些项负责色散，色散影响波的形状和传播。频散的研究在许多领域都很重要，包括地震学、声学和通信理论。本文提出了求解五阶非线性波动方程的三种有效解析方法。所采用的方法有修正辅助方程法、伯努利Sub-ODE法和G′/ G -展开法(MAE)。绘制了一些图表来显示我们的发现。非线性波动方程的解用于描述物理系统中波动的非线性动力学。结果表明，系统参数对波动解的动力学特性有很大的影响，可以作为系统的控制器。这项工作中使用的新方法有助于找到行波的新解。这可以看作是对该领域的新贡献。得到的解可以描述水波、等离子体波和声波的行为。 本文章由计算机程序翻译，如有差异，请以英文原文为准。 求助全文 约1分钟内获得全文 求助全文 来源期刊 Muenster Journal of Mathematics MATHEMATICS- 自引率 0.00% 发文量 0 相关文献 × 引用 GB/T 7714-2015 复制 MLA 复制 APA 复制 导出至 BibTeX EndNote RefMan NoteFirst NoteExpress × 求助内容： 期刊论文 学位论文 图书 其他 (专利、报告等) 只需要正文 仅需补充材料 应助结果提醒方式： 微信（请自行确认已关注Book学术公众号） 邮件 保存 保存后同步修改账户信息中的邮箱 确认发布求助 × 处理提示 您的部分求助已有人上传文件，您还尚未处理，请先处理完毕再发起新的求助 点击查看 × 努力提交中 提交成功 继续求助查看详情 × 提示 您的信息不完整，为了账户安全，请先补充。 现在去补充 × 没积分了 多种获得积分方式，供你选择！ 查看如何获取积分 × 提示 您因"违规操作" 具体请查看互助需知 我知道了 × 提示 现在去查看 取消 × 提示 确定 × 快捷登录 密码登录 用户名： 密码： 验证码： 两周内记住我 忘记密码？ 手机号： 验证码： 没有帐号？现在注册 请完成安全验证× 微信好友 朋友圈 QQ好友 复制链接 取消 已复制链接 快去分享给好友吧! 我知道了 点击右上角分享 0 $(function () { var title = $("#title").val(); var id = $("#id").val(); $.post("/Literature/GetRelatedLiterature", { id: id, title: title }, function (result) { if (result != null) { var html = ``; for (var i = 0; i < result.length; i++) { html += `<div class="sslist">`; html += `<a class="caption" href="` + $("#url1").val() + result[i].ArticleID + `.htm">` + result[i].Title + `</a>`; html += ` <div class="substance">`; html += `<span class="IF">IF ` + result[i].PeriodicalIF + ` </span>`; if (result[i].RegionNum > 0) { html += `<span class="fq` + result[i].RegionNum + `">` + result[i].RegionNum + `区 ` + result[i].RegionCategory + `</span>`; } //var EmployDataBaseShoreName = result[i].EmployDataBaseShoreName; //if (EmployDataBaseShoreName != "" && EmployDataBaseShoreName!=null) { // var names = EmployDataBaseShoreName.split('||') // for (var j = 0; j < names.length; j++) { // html += `<span class="fq5">` + names[j] + `</span>`; // } //} //html += ``; html += `</div>`; html += `<div class="substance">`; html += `<a href="` + $("#url2").val() + "_d" + result[i].PeriodicalID + `.htm" target="_blank">` + result[i].PeriodicalName + `</a>`; html += `<span class="Pub">Pub Date : ` + result[i].PublishDate + `</span>`; html += `</div>`; html += ` <div class="author">`; html += result[i].AuthorName; html += `</div>`; html += `</div>`; } if (html.length > 0) { $("#xglist").show(); $("#xglist").append(html); } } }); getReferenceCount(); }); function getReferenceCount() { var LocalId = localStorage.getItem("referenceName"); if (LocalId != null) { $.get("/Literature/GetBatchReferenceCountByLocalId", { LocalId: LocalId }, function (result) { $("#referencecount").html(result.Code); }, "json"); } else { $("#referencecount").html('0'); } } wx.config({ debug: false, appId: 'wx999b2eb01732df2e', timestamp: '1730880352', nonceStr: 'xfCk8OGlsXwLNeIu', signature: 'f62e99804e19882370531d322202f4f235e1378b', jsApiList: [ 'onMenuShareTimeline', 'onMenuShareAppMessage', 'hideMenuItems' ] });

Abstract

The fifth-order nonlinear wave equation contains terms involving higher-order spatial derivatives, such as u x x x and u x x x x x . These terms are responsible for dispersion, which affects the shape and propagation of the wave. The study of dispersion is important in many areas, including seismology, acoustics, and communication theory. In the current work, three potent analytical techniques are proposed in order to solve the fifth-order nonlinear wave equation. The used approaches are the modified auxiliary equation method, the Bernoulli Sub-ODE method, and the G ′ / G -expansion method (MAE). Some graphs are plotted to display our findings. The solutions to the nonlinear wave equation are used to describe the nonlinear dynamics of waves in physical systems. The results show how the dynamics of the wave solutions are influenced by the system parameters, which can be used as system controllers. The new approaches used in this work helped to find new solutions for traveling waves. This could be seen as a new contribution to the field. Water waves, plasma waves, and acoustic wave behavior can be described by the obtained solutions.