Conference on Nonlinear Waves: Analysis and Applications

该奖项支持参加将于2017年3月17-19日在匹兹堡大学举行的《非线性波：分析与应用》会议。非线性波在自然界中无处不在。例如水波、声学、太阳风、材料和激光中的振动波以及神经脉冲的传播等等。这些不同类型的现象可以用基于双曲型、椭圆型和色散型偏微分方程式的数学模型来描述，这些模型彼此惊人地相似。然而，数学方程的求解是极其困难的；事实上，非线性波动被认为是偏微分方程分析中最重要的问题之一。尽管在过去的几十年里，这一领域取得了长足的进步，但在物理、工程、工业、材料科学、生物等领域也出现了新的重要和具有挑战性的问题。会议的目标是汇聚非线性波各个理论和应用领域的顶尖专家，以促进和加强统一技术，建立新的联系，并促进不同应用领域的交叉受精。相关的世界级专家和专家将在大会上进行研究报告。会议将为学生和初级研究人员提供机会，包括那些来自数学小组中代表性不足的小组的学生，以了解该领域的最新成果，并介绍他们的最新研究成果。大会将通过讲座、网页、传单、海报等形式传播研究成果，宣传研究领域。会议的网址是www.math.bitt.edu/~dwang/pde2017.html。会议将讨论在水波、动力学理论、拓扑绝缘体和超材料等新介质中的波、非线性光学中的波和凝聚态物理等方面的最新突破性工作和取得的实质性进展。发现了许多意想不到的联系，将这些问题彼此联系起来，和/或与偏微分方程其他领域的问题联系起来，并与以前似乎互不相关或相互影响很小的新兴应用联系在一起。这使得这次会议特别及时。

This award supports participation in the conference "Nonlinear Waves: Analysis and Applications", to be held at the University of Pittsburgh on March 17-19, 2017. Nonlinear waves are ubiquitous in nature. Examples include water waves, acoustics, the solar wind, vibrational waves in materials and laser beams, and propagation of nerve impulses, among many others. These disparate types of phenomena can be described by mathematical models that are based on hyperbolic, elliptic and dispersive partial differential equations and that are surprisingly similar to each other. However, the mathematical equations are extremely difficult to solve; in fact the nonlinear waves are considered as one of the most important problems in the analysis of partial differential equations. Although considerable progress has been made in the field over the past few decades, new important and challenging problems have been emerging in physics, engineering, industry, material sciences, biology, and other fields. The goal of the conference is to bring together leading experts in various theoretical and applied aspects of nonlinear waves to promote and enhance unifying techniques, to establish new connections, and to foster cross-fertilization among different fields of application. Relevant world-class experts and specialists will give research talks at the conference. The conference will provide an opportunity for students and junior researchers, including those from underrepresented groups in mathematics groups to get abreast with the latest achievements in the field and present their recent research results. The conference will disseminate research results and promote the research area through talks, webpage, flyers, and posters. The conference web site is www.math.pitt.edu/~dwang/pde2017.htmlThe conference will discuss the recent breakthrough work and substantial progress achieved in the following directions: water waves, kinetic theory, waves in novel media such as topological insulators and metamaterials, waves in nonlinear optics and condensed matter physics, and so on. Many unexpected connections were discovered linking these problems to each other, and/or to problems in other areas of partial differential equations and to emerging applications which previously appeared unrelated or had little impact on one another. This makes the conference especially timely.