## Contact InformationI am a postdoctoral researcher working at Northumbria University in the MCNP group of the department of Mathematics, Physics and Electrical Engineering.Address:Department of Mathematics, Physics and Electrical Engineering Northumbria University Ellison Place Newcastle-upon-Tyne NE1 8ST United Kingdom Mail: thibault.congy at northumbria.ac.ukShort CV List of publications |

I am currently working on a new realization of the wave-mean flow interaction whereby a linear wave packet is incident on a evolving large-scale nonlinear hydrodynamic state: a rarefaction wave or a dispersive shock wave. Modulation equations can be derived for the coupling between the linear wavepacket and the mean flow in the dispersive hydrodynamic state. Through the resolution of these equations, conditions for the transmission or the trapping of the incident wave by the unsteady hydrodynamic state can be determined. | |

A dispersive shock wave (DSW) is an expanding, modulated nonlinear wavetrain which can be viewed as a dispersive counterpart to the dissipative, classical shock. The nonlinear SchrÃ¶dinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains. Taking advantage of the overlapping asymptotic regime that applies to both the NLS and Whitham modulation descriptions, we are developing a universal analytical description of DSWs for a broad class of physically relevant systems. |

For my PhD project, I studied self-accelerating 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 ring-shaped optical caustic, which, following reflection from the boundary, converges to a focal point. By means of a semi-classical treatment, we have demonstrated that the radially symmetric wave has an Airy-function profile. | |

I have also been interested in nonlinear effects in two-component Bose-Einstein condensates in one dimension. In the presence of spin-orbit coupling, excitations of the polarization degree of freedom experience modulational instability also known as the Benjamin-Feir instability. In the limit where intra-species and inter-species interaction constants are very close, the density dynamics and the polarization dynamics decouple, the latter being governed by the dissipationless Landau-Lifshitz equation. So-called magnetic solitons and dispersive shock waves (see figure opposite) are observed in this system, among other nonlinear structures. |