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

机译:多相调制中的双重退化与Boussinesq方程的出现

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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”>摘要近年来,守恒定律奇异性,或线性惠特姆方程中出现的更普遍的零特征,与简化非线性偏微分方程(PDE)的出现之间的联系由拉格朗日密度所产生的系统,在保守系统中已经得到。值得注意的是,守恒定律构成了简化非线性系统的一部分。本文研究了多相波列中的双简并情况,其特征是线性化惠特姆系统的双零特性,由此产生的相对平衡调制(这是波列调制的推广)导致矢量双向Boussinesq方程。导出的偏微分方程与之前的结果(如[1])一致,因为除了一个系数外,它的所有系数都与沿相对平衡解的守恒定律有关,然后这些守恒定律被投影形成相应的标量系统。该理论被应用于两个例子,以强调如何评估临界性,以及如何获得双向Boussinesq方程的系数。第一个是耦合非线性薛定谔(NLS)系统,这是首次证明双向Boussinesq方程在这种情况下出现,第二个是分层浅水模型,该模型根据现有结果验证了理论 </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 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