Dynamics in spatially confined Hamiltonian systems

When a stone is dropped into a still (infinitely large) pond, concentric ripples flow outwards from the splash carrying the energy away and consequently the pond settles back to rest. For a finite pool the behavior is very different: outgoing waves bounce back to the walls and return to the interior giving rise to complex nonlinear wave interactions. For this reason, the understanding of propagation of nonlinear waves in spatially connected systems is much more challenging than in spatially unbounded systems. The aim of the project is to develop theoretical tools for describing such systems and to apply them to physical models. The key phenomenon that needs to be addressed and understood is the wave turbulence in which the waves develop structures at smaller and smaller scales in the course of evolution. Our investigations have the potential of the real world applications, for example in engineering efficient ways of sending signals through fiber optics cables or in predicting the properties of atomic gases cooled down to temperatures near absolute zero.

Project in the National Science Centre database