Geometric analysis of transcendental solutions of nonlinear systems

Summary

Modern science derives its power from mathematics. The project aims to capture, identify and describe pivotal, transcendental solutions of nonlinear systems that are universal in science, in the sense that they always arise as mathematical models under certain physical limits. The project expects to produce new mathematical methods to describe such functions by using a newly discovered geometric framework.

Supervisor(s)

Professor Nalini Joshi, Dr Milena Radnovic

Research Location

School of Mathematics and Statistics

Program Type

PHD

Synopsis

The project will construct initial value spaces of nonlinear systems to pursue questions that fall within three areas:
• analytic properties of solutions;
• asymptotic properties of solutions;
• connections to mathematical billiards.
The construction is made possible by the fact that these solutions parametrise curves that travel through the space of all possible initial values. The method of construction is non-trivial, requiring geometric methods called resolution or blow-up at places where the flow of the system becomes undefined.
Important open problems include the search for patterns of poles in solutions.

Additional Information

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Keywords

Ordinary Differential Equations, difference equations, dynamical systems, Approximation Theory, Asymptotic Methods, Integrable systems

Opportunity ID

The opportunity ID for this research opportunity is: 2768

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