The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $160,000 Project Grant to The Regents of the University of Colorado (doing business as the University of Colorado) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports fundamental research into nonlinear wave propagation, focused on enhancing scientific understanding of large amplitude waves and associated wave energy transfer dynamics. This work has potential applications for...
This Project Grant award of $199,995 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research on nonlinear wave propagation and formation. The project aims to develop mathematical tools to identify and characterize emergent asymptotic phenomena in nonlinear wave models, with a focus on non-generic or anomalous behavior. Key goals include understanding mechanisms behind anomalously slow decay in integrable wave equation solutions,...
This three-year, $295,778 Project Grant from the National Science Foundation's Division of Mathematical Sciences will support research addressing long-standing problems in the nonlinear propagation of waves. The principal investigator and collaborators at the University of Chicago will conduct mathematical studies of soliton resolution for energy critical nonlinear wave equations and related models, both with and without symmetries. Quantitative unique continuation properties with connections to...
This Project Grant award of $300,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research on the stability and behavior of large amplitude relaxation waves. The Principal Investigator will study key open problems related to the stability and behavior of shallow water waves, including phenomena like destructive rogue waves and herringbone flow patterns, using a blend of finite- and infinite-dimensional dynamical systems tools...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
This $282,599 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences will support research into validated numerical methods for studying the stability of nonlinear wave phenomena. The investigators will focus on establishing the stability of periodic traveling wave solutions to various Hamiltonian partial differential equations (PDEs), including the generalized Korteweg-de Vries (KdV) and nonlinear Schrödinger equations. Key objectives include...
This $350,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports the development of robust and efficient numerical algorithms for solving nonlinear second-order wave equations. The research aims to create computational tools that can accurately simulate a wide range of wave phenomena in areas such as geophysics, plasma physics, and quantum science. The project focuses on constructing fully discrete,...
This $343,401 Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports research on nonlinear dispersive flows at the University of Wisconsin-Madison. The primary objective is to examine solutions to a broad class of nonlinear wave equations that model physical phenomena in fields such as fluid dynamics, quantum mechanics, and general relativity. The research will investigate...
This $388,536 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences, under the Mathematical and Physical Sciences (CFDA 47.049) program, supports fundamental research at the University of Massachusetts (UMass) to study the propagation of randomness in nonlinear wave phenomena. The key objectives of the 3-year project are to: Analyze the long-term dynamics and stability of dispersive flows from a probabilistic perspective in energy subcritical regimes....
This $186,811 Project Grant was awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences to Georgetown University on September 1, 2024. The grant supports research on "Analytical Challenges Near Dynamical Thresholds for Nonlinear Wave and Fluid Equations" over a 3-year period through August 31, 2027. The research aims to develop a deeper understanding of the mathematical behavior of partial differential equations that model a variety of physical systems,...