Parametric form of QCD travelling waves

Stability of Travelling Waves

Stability of travelling waves

An overview of various aspects related to the spectral and nonlinear stability of travelling-wave solutions to partial differential equations is given. The point and the essential spectrum of the linearization about a travelling wave are discussed as is the relation between these spectra, Fredholm properties, and the existence of exponential dichotomies (or Green’s functions) for the linear ope...

Synaptic travelling waves

An important goal of neuroscience is to establish a series of direct links between the abstract nature of biophysical model equations and their interpretation in terms of experimental findings in biological neural networks. I propose to address this issue by developing a novel mathematical analysis of the dynamics of synaptically interacting neural systems and by establishing a framework for co...

Travelling waves in multivortex configurations

We investigate zero modes of a multivortex background which are due to the energetic degeneracy of the planar static n-vortex solution in Bogomol’nyi limit of the Abelian Higgs model parametrised by a set of 2n real parameters. The zero modes take the form of waves travelling with a speed of light independently along each of the vortices irrespectively to their mutual separations. String descri...

Torsional Travelling Waves in DNA

The simple model of the non-linear DNA dynamics [4] is pursued in order to study the local untwisting of DNA double helix. It is shown how the advancing RNA polymerase may force the motion of the torsional solitary wave along DNA.