**"...the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations..."**

**W. Heisenberg, Nobel Laureate 1932**

Nonlinear equations describe fundamental physical phenomena in nature ranging from chaotic behaviour in biological systems, plasma containment in tokamaks and stellarators for energy generation, to solitonic fibre optical communication devices. The Nonlinear Phenomena Group at UNSW is world-renowned for its work in soliton theory and dynamical systems and attracts visitors of international repute in these areas on a regular basis. The research programme of the group involves the analysis of complex physical and biological systems and the systematic investigation of potential new areas of application of modern soliton theory in magneto-hydrodynamics, the fabrication of fibre-reinforced composites and elastic shell structure design.

### Research Interests

- Solutions to nonlinear systems (approximation, numerical and exact methods)
- Fluid mechanics and differential equations
- Nonlinear hydrodynamic stability
- Nonlinear dynamics and stability
- Nonlinear lattice dynamics and non-equilibrium growth models
- Superintergrable systems
- Differential geometry and symmetries of wave equations
- Solar modelling
- Elliptic partial differential equations in mathematical, physical and biological sciences
- Geometric structure of soliton systems both discrete and continuous
- Infinitesimal and finite Bäcklund transformations
- Hidden solitonic structures in nonlinear continuum mechanics
- Reciprocal transformations and moving boundary value problems
- General relativity
- Dynamic equations on time scales
- Lie-algebraic study of symmetries of nonlinear systems of physical interest
- Discrete integrable dynamical systems
- Symmetry and time-reversal symmetry in dynamical systems
- Dynamical systems arising from quasiperiodic physical phenomena
- Algebraic dynamics (group theoretic/number theoretic approaches to dynamical systems)
- Inequalities - differential, difference, dynamic and integral
- Differential inclusions
- Transfer operators and Perron-Frobenius operators
- Smooth and numerical ergodic theory
- Stochastic modelling and fractional calculus

### Group Members

- Christopher Angstmann
- Gary Froyland
- Bruce Henry
- Jonathan Kress
- John Roberts
- Wolfgang Schief
- John Steele
- Chris Tisdell
- Peter Blennerhassett

### Research Fellows

- Jason Atnip

### Relevant Courses

### Links

- Computational Neurobiology and Imaging Centre, Mount Sinai School of Medicine, New York
- CRC 701: Spectral Structures and Topological Methods in Mathematics
- DFG Research Center - Mathematics for Key Technologies