Turbulent steady states in the nonlinear Schrodinger equation.

Abstract: The nonlinear Schrodinger (NLS) equation, also known as the Gross-Pitaevskii equation, is one of the most common equations in physics. Its applications go from the propagation of light in nonlinear media to the description of gravity waves and Bose-Einstein condensates. In general, the NLS equation describes the evolution of nonlinear waves. Such waves interact and transfer energy and other invariants along scales in a cascade process. This phenomenon is known as wave turbulence and is described by the (weak) wave turbulence theory (WWT). One of the most significant achievements of WWT is the complete analytical characterization of turbulent steady states obtained in the long time limit when the system contains forcing and dissipative terms acting on well-separated scales.

In the first part of my seminar, I will briefly introduce the theory of wave turbulence in the case of the NLS equation and the derivation of its associated kinetic equation describing the evolution of the wave spectrum (the variance of the solution Fourier transform). Then, I will present recent theoretical developments on the steady-state solutions of the 3D NLS equation. Those new predictions are validated using high-resolution numerical simulations of the 3D NLS equation and its associated wave kinetic equation.

Posted on Jan 19, 2023 in Seminar CMM, Seminars