Contact InformationInstitution:Department of Mathematical Sciences Loughborough University Loughborough, Leicestershire LE11 3TU Group: Linear and nonlinear waves Mail: t.congy at lboro.ac.uk Short CV: PDF 

For my PhD project, I studied selfaccelerating Airy beams with the experimental group of S. Barad (Tel Aviv University). These nondiffracting auto  accelerating waves have received considerable attention in recent years. We showed that they can form spontaneously as a laser beam propagates in a defocusing nonlinear medium, inside a cylindrical channel with a reflective boundary. The beam forms a ringshaped optical caustic, which, following reflection from the boundary, converges to a focal point. By means of a semiclassical treatment, we have demonstrated that the radially symmetric wave has an Airyfunction profile.  
I have also been interested in nonlinear effects in twocomponent BoseEinstein condensates in one dimension. Using a muliple scale expansion, we have shown that these condensates experience phenomena similar to those encoutered in fluid mechanics or nonlinear optics. Nonlinear density excitations are well described by a KdVtype equation. In the presence of spinorbit coupling, excitations of the polarization experience modulational instabilities also known as the BenjaminFeir instability.  
In the limit where intraspecies and interspecies interaction constants are very close, the dynamics of the density and the polarization waves decouple. The polarization wavedynamics is governed by the dissipationless LandauLifshitz equation. Dispersive shock waves (DSW) can be observed in this system. Thanks to the Whitham theory of waves modulation, we have described the DSW within the GurevitchPitaevskii scheme. The DSW can be seen as a nonlinear periodic wave for which its parameters (amplitude, velocity, ...) vary slightly over one period of space and time.  
In 2013 I did a 3 months internship at Trento. Under the supervision of F. Dalfovo, I studied the stability of solitons in twodimensional BoseEinstein condensate. Grey solitons in condensate with repulsive interractions undergo a dynamical instability for long wavelength transverse excitations. This phenomenon is called « snake oscillations ». Numerical simulation of the 2D GrossPitaevkii equation for an initial 1D darksoliton profile (k represents the wavenumber of the transverse excitation) k=30 (WEBM GIF) k=60 (WEBM GIF) 