Mathematical Breakthroughs in Wave Propagation

本理论数学奖学金提案旨在解决波传播中的三个主要开放问题。这些是非线性波的长期行为，包括孤立波的行为和相互作用；波浪在粗糙介质中的传播；以及在混沌射线动力学假设下相互作用波的小尺度行为。这项研究的目的是分析在光学介质和波导、医学和地震成像以及纳米电子设备中模拟问题的波动方程。预计将在新的数学理论、澳大利亚的研究能力、更好的数值计算波的算法以及通信、医学成像和地震成像方面的技术进步方面取得成果和效益。

This Fellowship proposal in theoretical mathematics aims to solve three major open problems in wave propagation. These are the long-time behaviour of nonlinear waves, including the behaviour and interaction of solitary waves; the propagation of waves in rough media; and the small-scale behaviour of interacting waves under the assumption of chaotic ray dynamics. The research aims to analyse wave equations that model problems in optical media and waveguides, medical and seismic imaging, and nano-electronic devices. Outcomes and benefits are expected in new mathematical theory, Australian research capability, better algorithms for numerically computing waves, and technological advances in communications, medical imaging, and seismic imaging.