Conference on Nonlinear Waves: Analysis and Applications

该奖项支持参加将于2017年3月17日至19日在匹兹堡大学举行的“非线性波：分析和应用”会议。非线性波在自然界中普遍存在。例子包括水波，声学，太阳风，材料和激光束中的振动波，以及神经脉冲的传播等等。这些不同类型的现象可以通过基于双曲、椭圆和色散偏微分方程的数学模型来描述，并且这些数学模型彼此惊人地相似。然而，数学方程是非常困难的解决，事实上，非线性波被认为是最重要的问题之一，在分析偏微分方程。尽管在过去的几十年里，该领域取得了相当大的进展，但在物理学、工程学、工业、材料科学、生物学和其他领域，新的重要和具有挑战性的问题不断出现。会议的目标是汇集非线性波的各种理论和应用方面的领先专家，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之间的交叉施肥。有关世界级的专家和专家将在会议上发表研究报告。会议将为学生和初级研究人员提供一个机会，包括那些来自数学组代表性不足的群体，以了解该领域的最新成就，并介绍他们最近的研究成果。会议将通过讲座、网页、传单和海报传播研究成果并推广研究领域。会议网址为www.math.pitt.edu/~dwang/pde2017.htmlThe会议将讨论近期的突破性工作和取得的实质性进展，主要方向如下：水波、动力学理论、拓扑绝缘体和超材料等新介质中的波、非线性光学和凝聚态物理中的波等等。许多意想不到的联系被发现将这些问题彼此联系起来，和/或偏微分方程的其他领域中的问题以及先前看起来不相关或彼此影响很小的新兴应用。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.