Section: New Results

Numerical simulation of traveling waves for some nonlocal Gross-Pitaevskii equations with nonzero conditions at infinity in dimensions 1 and 2

As a follow-up of the previous result, P. Mennuni and G. Dujardin carried out numerical simulations of traveling waves for some nonlocal nonlinear Gross-Pitaevskii equations with nonzero conditions at infinity in dimensions 1 and 2. Using a numerical analogue of the minimization of the energy at fixed momentum, they used gradient methods with nonuniform fast Fourier transforms (to deal with the nonlocal terms numerically) to carry out significant numerical simulations to illustrate numerically the theoretical results and to discuss the hypotheses numerically. These results can be found in P. Mennuni's PhD manuscript [10].