Weak and strong optical turbulence in the Schrödinger Helmholtz Equation

Tuesday 03, 17:15

Jonathan Skipp

Aston university

In this talk I will give an overview of results that Sergey has led us to, on the Schrödinger Helmholtz Equation (SHE). The SHE is a model that describes nonlinear optics beyond the Kerr regime (it also has applications to cosmology, modelling dark matter as an ultra low-mass boson). As such, it is an extension of the familiar nonlinear Schrödinger equation, incorporating a spatially nonlocal self-potential. In 1D, we have examined how the non-integrability of the SHE leads to interesting dynamics of solitons: interactions with weakly nonlinear waves, generation of bound soliton states, and soliton mergers. I will show how a tool borrowed from integrable systems theory, the direct scattering transform, can be used to help characterise these dynamics, even when the system is quite far from being integrable. In 2D I return to wave turbulence, and will summarise how the SHE has a nonlinearity that allows for a reduction of the collision integral into a much simpler form, and the cascade solutions found. This is the first time in the wave turbulence literature that a reduced kinetic model can be obtained fully analytically.


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Slides


Jonathan Skipp