Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation

Ratliff Daniel J.

摘要

Abstract >In recent years, a connection between conservation law singularity, or more generally zero characteristics arising within the linear Whitham equations, and the emergence of reduced nonlinear partial differential equations (PDEs) from systems generated by a Lagrangian density has been made in conservative systems. Remarkably, the conservation laws form part of the reduced nonlinear system. Within this paper, the case of double degeneracy is investigated in multiphase wavetrains, characterized by a double zero characteristic of the linearized Whitham system, with the resulting modulation of relative equilibrium (which are a generalization of the modulation of wavetrains) leading to a vector two‐way Boussinesq equation. The derived PDE adheres to the previous results (such as [1]) in the sense that all but one of its coefficients is related to the conservation laws along the relative equilibrium solution, which are then projected to form a corresponding scalar system. The theory is applied to two examples to highlight how both the criticality can be assessed and the two‐way Boussinesq equation's coefficients are obtained. The first is the coupled Nonlinear Schrodinger (NLS) system and is the first time the two‐way Boussinesq equation has been shown to arise in such a context, and the second is a stratified shallow water model which validates the theory against existing results. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract xmlns =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”> <title type =“main”> xpractt </ title> >最近多年来，在线性WHITHAM方程中，在线性WHITHAM方程中产生的保护法奇异性，或者更通常零特征，以及由拉格朗日密度产生的系统产生的减少的非线性偏微分方程（PDE）的出现已经在保守的系统中进行。值得注意的是，保护法则构成了减少的非线性系统的一部分。在本文中，在多相波形中研究了双退化的情况，其特征在于线性化WHITHAM系统的双零特征，得到了相对平衡的调制（这是波动调节的泛化），导致矢量二 - 道路Boussinesq方程。衍生的PDE在其所有系数与沿着相对平衡溶液的保护规律相关的意义上涉及先前的结果（例如[1]），然后投影以形成相应的标量系统。该理论应用于两个示例，以突出如何评估临界程度，并且获得双向Boussinesq公式的系数。首先是耦合非线性Schrodinger（NLS）系统，并且是在这样的上下文中显示出双向Boussinesq方程的第一次，第二是分层浅水模型，验证了现有结果的理论。< / p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-29329/'>《Studies in Applied Mathematics》</a> <b style="margin: 0 2px;">|</b><span>2018年第1期</span><b style="margin: 0 2px;">|</b><span>共30页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ratliff Daniel J.&option=202" target="_blank" rel="nofollow">Ratliff Daniel J.;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>University of Surrey;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1147.html" title="应用数学">应用数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> </p> </li> </ul> </div> </div> <div class="literature cardcommon" id="literaturereference" style="display:none"> <div class="similarity "> <h3 class="all_title" id="enpatent111">引文网络</h3> <div class="referencetab clearfix"> <ul id="referencedaohang"> <li dataid="referenceul">参考文献</li> <li dataid="citationul">引证文献</li> <li dataid="commonreferenceul">共引文献</li> <li dataid="commoncitationul">同被引文献</li> <li dataid="tworeferenceul">二级参考文献</li> <li dataid="twocitationul">二级引证文献</li> </ul> </div> <div class="reference_details" id="referenceList"> <ul id="referenceul"></ul> <ul id="citationul"></ul> <ul id="commonreferenceul"></ul> <ul id="commoncitationul"></ul> <ul id="tworeferenceul"></ul> <ul id="twocitationul"></ul> </div> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024473339.html">Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ratliff Daniel J.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Ratliff Daniel J. </a> <a href="/journal-foreign-29329/" target="_blank" rel="nofollow" class="tuijian_authcolor">Studies in Applied Mathematics .</a> <span>2018</span><span>,第1期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：多相调制中的双重退化与Boussinesq方程的出现</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-cn_mathematical-research-application-english_thesis/0201221467970.html">Double Traveling Wave Solutions of the Coupled Nonlinear Klein-Gordon Equations and the Coupled SchrSdinger-Boussinesq Equation</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Lanfang SHI1&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Lanfang SHI1,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ziwen NIE12&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Ziwen NIE12 </a> <a href="/journal-foreign-22871/" target="_blank" rel="nofollow" class="tuijian_authcolor">数学研究及应用：英文版 .</a> <span>2017</span><span>,第006期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：耦合的非线性Klein-Gordon方程和耦合的SchrSdinger-Boussinesq方程的双行波解</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070409988531.html">Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ratliff Daniel J.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Ratliff Daniel J.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bridges Thomas J.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Bridges Thomas J. </a> <a href="/journal-foreign-29321/" target="_blank" rel="nofollow" class="tuijian_authcolor">Physica, D. Nonlinear phenomena .</a> <span>2016</span><span>,第Null期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Whitham调制方程，合并特性和色散Boussinesq动力学</span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-conference-foreign_meeting-275185_thesis/0705015194676.html">Oscillation Properties of the Equation of Boussinesq and Comparison with Other Fourth Order Equations</a> <b>[C]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Z. Petrova&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Z. Petrova </a> <a href="/conference-foreign-275185/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Conference on Application of Mathematics in Technical and Natural Sciences .</a> <span>2009</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Boussinesq方程的振动性质及其与其他四阶方程的比较</span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/academic-degree-foreign_mphd_thesis/02061740821.html">Global dynamics of dissipative generalized KdV equations and Boussinesq equations</a> <b>[D] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Cao, Jun&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Cao, Jun </a> <span>1994</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：耗散广义KdV方程和Boussinesq方程的整体动力学</span> </p> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-journal-foreign-pmc_detail_thesis/040004607387.html">Multiphase wavetrains singular wave interactions and the emergence of the Korteweg–de Vries equation</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Daniel J. Ratliff&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Daniel J. Ratliff,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Thomas J. Bridges&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Thomas J. Bridges </a> <span>-1</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：多相波列奇异波相互作用和Korteweg-de Vries方程的出现</span> </p> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/open-access_resources_thesis/0100028527037.html ">Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation</a> <b>[O] </b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ratliff, Daniel&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Ratliff, Daniel </a> <span>2017</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：多相调制中的双重简并性和Boussinesq方程的出现</span> </p> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/academic-journal-cn_communication-television_thesis/0201230244097.html">双重调制及晶体管集电极双重调制</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=郭凌野&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 郭凌野</a> <span> <a href="/journal-cn-27414/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 通信与电视 </a> </span> <span> . 1989</span><span>,第004期</span> </span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-cn_journal-chongqing-technology-business-university-natural-science-edition_thesis/0201273310288.html">随机δ冲击下多相关退化的竞争失效可靠性评估</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘汉葱&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 刘汉葱</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘赪&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,刘赪</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张诚&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,张诚</a> <span> <a href="/journal-cn-4532/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 重庆工商大学学报（自然科学版） </a> </span> <span> . 2019</span><span>,第005期</span> </span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/academic-journal-cn_journal-chongqing-institute -technology_thesis/0201273063400.html">随机冲击下多相关退化的竞争失效可靠性模型</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘汉葱1&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 刘汉葱1</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=唐家银1&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,唐家银1</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘赪1&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,刘赪1</a> <span> <a href="/journal-cn-55209/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 重庆理工大学学报 </a> </span> <span> . 2019</span><span>,第006期</span> </span> </div> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-journal-cn_optical-communication-technology_thesis/0201288862304.html">RoF系统中基于双重幅度调制的载波重用技术</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=狄晗&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 狄晗</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=陈新桥&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,陈新桥</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘晓蕊&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,刘晓蕊</a> <span> <a href="/journal-cn-8736/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 光通信技术 </a> </span> <span> . 2021</span><span>,第003期</span> </span> </div> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/academic-journal-cn_radio-television-information_thesis/0201279282936.html">双重副载波调制在调频多工广播中的应用</a> <b>[J]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=阿里木·阿不都热合曼&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 阿里木·阿不都热合曼</a> <span> <a href="/journal-cn-8727/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 广播电视信息 </a> </span> <span> . 2020</span><span>,第005期</span> </span> </div> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-conference-cn_meeting-59181_thesis/020222590145.html">基于双重规整化的气动光学效应退化图像盲复原算法</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=何成剑&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 何成剑</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=洪汉玉&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,洪汉玉</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=张天序&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,张天序</a> <span> <a href="/conference-cn-59181/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 二〇〇六年全国光电技术学术交流会 </a> <span> <span> . 2006</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020316453345.html">试谈双重否定“不X不”格式出现的篇章语义环境</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=代严严&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 代严严</a> <span> . 2010</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120111974107.html">一种基于空间调制偏振成像的在宽波段偏振成像中避免出现混叠的入射光带宽的确定方法</a> <b>[P]</b> . <span> 中国专利： CN111953423A </span> <span> . 2020-11-17</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120202996731.html">调制域分析仪中的多相计数电路</a> <b>[P]</b> . <span> 中国专利： CN202998061U </span> <span> . 2013.06.12</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130403234861.html">An analysis method of waves propagating at Variable Water Depth using the Standard Boussinesqs Equations</a> <b>[P]</b> . <span> 外国专利：  KR20190105261A </span> <span> . 2019-09-17</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用标准Boussinesqs方程分析在可变水深处传播的波浪的方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130405977462.html">NUMERICAL ANALYSIS METHOD OF IMPROVED BOUSSINESQ EQUATION</a> <b>[P]</b> . <span> 外国专利：  KR20180097982A </span> <span> . 2018-09-03</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：改进的Boussinesq方程的数值分析方法 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130472137037.html">TEACHING AID FOR DOUBLE LINEAR SIMULTANEOUS EQUATIONS</a> <b>[P]</b> . <span> 外国专利：  JPS61145580A </span> <span> . 1986-07-03</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：双线性联立方程组的教学辅助 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704024473339','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div class="journalsub-pop-up" style="display: none"> <div class="journal-sub"> <h2>期刊订阅</h2> <img src="https://cdn.zhangqiaokeyan.com/img/loginclose.png" alt="关闭" onclick="$('.journalsub-pop-up').hide()"> <p class="pardon">抱歉，该期刊暂不可订阅，敬请期待！</p> <p class="current">目前支持订阅全部北京大学中文核心（2020）期刊目录。</p> <div style="display: flex;margin-top: 69px;justify-content: space-between;"> <div class="no-sub" onclick="$('.journalsub-pop-up').hide()">暂不订阅</div> <div class="other-sub" onclick="continueSub('from=pc-detail')">继续订阅其他期刊</div> </div> </div> </div> <div class="right_btn"> <ul> <li class="gouwuche">  </li> <li class="yijian"> <a href="javascript:void(0);" onclick="link_analysis('/mycenter/auth/complaint.html',this)" title="意见反馈">意见反馈</a> </li> <li class="top"> <a href="javascript:scrollTo(0,0);" title="回到顶部">回到顶部</a> </li> <li class="shouye"> <a href="/" title="首页">回到首页</a> </li> </ul> </div> <div class="xllindexfooter"> <div class="xllindexfootercenter"> <div class="xllindexfooterleft left" > <div class="xllindexfooterleftli"> <ul> <li><a href="/about.html" title="关于掌桥">关于掌桥</a></li> <li><a href="/help/helpmap.html" title="资源导航">资源导航</a></li> <li><a href="/help/helpguide.html" title="新手指南">新手指南</a></li> <li><a href="/help/helpcenter.html" title="常见问题">常见问题</a></li> <li><a href="/sitemap.html" title="网站地图">网站地图</a></li> <li><a href="/help/helpcenter.html?type=9" title="版权声明">版权声明</a></li> </ul> </div> <div class="xllindexfooterleft"> <p class="xllindexfooterlefteamil">客服邮箱：kefu@zhangqiaokeyan.com</p> <div class="xllindexfooterlefttcp"> <div class="xllindexfooterpoliceiimg"></div> <div class="xllindexfooterpoliceispan"> <span>京公网安备：11010802029741号 </span> <span>ICP备案号：<a href="https://beian.miit.gov.cn" rel="nofollow" target="_blank" title="ICP备案号">京ICP备15016152号-6</a></span> <span>六维联合信息科技 (北京) 有限公司©版权所有</span> </div> </div> </div> </div> <div class="xllindexfooterright left"> <ul> <li> <p style="font-weight: bold;">客服微信</p> <div></div> </li> <li> <p style="font-weight: bold;">服务号</p> <div></div> </li> </ul> </div> </div> </div> <span id="0704024473339down" data-source="7," data-out-id="C2yLvLfp3a8gOHi43x/zcA==," data-f-source-id="7" data-title="Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation" data-price="20" data-site-name="" data-transnum="24" style="display:none;"></span> <input type="hidden" value="4" id="sourcetype"> <input type="hidden" value="0704024473339" id="docid"> <input type="hidden" value="29329" id="journalid"> <input type="hidden" value="1" id="inyn_provide_service_level"> <input type="hidden" value="https://cdn.zhangqiaokeyan.com" id="imgcdn"> <input type="hidden" value="1" id="isdeatail"> <input type="hidden" value="" id="syyn_indexed_database"> <input type="hidden" value="" id="servicetype"> <input type="hidden" id="pagename" value="Double Degeneracy in Multiphase Modulation and the Emergence of the Boussinesq Equation"/> <input type="hidden" value="thesis_get_original" id="pageIdentification"> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/jquery-1.12.4.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/lwlh_ajax.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zq.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/common.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/jquery.cookie.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/top.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/tip.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/login.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/down.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/search.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/newmail.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/page.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/searchtype.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/user/regist.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zxs_solor/detail.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/zxs_solor/reference.js?v=5.8.7"></script> <script type="text/javascript" src="https://www.zhangqiaokeyan.com/statistics/static/pagecollection.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/tj.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/sse.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/pushbaidu.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/common/history.js"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/util/cookie.js?v=5.8.7"></script> <script type="text/javascript" src="https://cdn.zhangqiaokeyan.com/js/weipu/weipu.js?v=5.8.7"></script> </body> <script> function kefu(customization) { var from = GetQueryString("from"); if (from == null || from == "") { from = "other"; } var url = getWxWorkQrCode(73, from, customization); if (url == "" || typeof url == 'undefined') { url = "https://wework.qpic.cn/wwpic/994838_0LUTS-VqR0quT1N_1675665967/0"; } tipDocGuidance(url, '人工辅助获取外文期刊材料'); } $(function(){ var weiPuStatus = getCookie('WeiPuStatus'); if(weiPuStatus){ tipWeiPuStatus(weiPuStatus); delCookie('WeiPuStatus'); } getFacetKeywordVoInId(); var sourcetype = $("#sourcetype").val(); var inyn_provide_service_level = $("#inyn_provide_service_level").val(); if((sourcetype ==1||sourcetype==4)&&inyn_provide_service_level!=4){ getJournal(); } }) function toCoverPage(){ var sourcetype=$("#sourcetype").val var fromStr=""; if(sourcetype==0){ fromStr="pc-wwoaxiangqing"; } if(sourcetype==4){ fromStr="pc-wwdetail-title"; } if(sourcetype==5){ fromStr="pc-wwhuiyixiangqing"; } window.location.href=url+"/zhichengpingshenlunwen.html?from="+fromStr; } </script> </html>