The Maslov Index for non-Hamiltonian systems. This project will uncover how the shape and structure (geometry) of solutions to partial differential equations influence how they change over time. By fo

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The Maslov Index for non-Hamiltonian systems. This project will uncover how the shape and structure (geometry) of solutions to partial differential equations influence how they change over time. By focusing on the inherent geometry of these systems, the project will deepen our understanding of how non-conservative systems behave dynamically. Key outcomes include: insights into the behavior of stable, coherent patterns; a clearer understanding of how spatial patterns interact with time-based changes in systems; and innovative applications of classical mathematical methods to complex systems involving multiple scales. These findings will advance modeling and analysis, with practical applications in fields such as nanotechnology, superconductors, and non-linear optics.. Scheme: Discovery Projects. Field: 4904 - Pure Mathematics. Lead: A/Prof Robert Marangell