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math.NA2025
High order uniform in time schemes for weakly nonlinear Schrödinger equation and wave turbulence
Quentin Chauleur, Antoine Mouzard
We introduce two multiscale numerical schemes for the time integration of weakly nonlinear Schrödinger equations, built upon the discretization of Picard iterates of the solution.…
math.NA2024
Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation
Quentin Chauleur, Radu Chicireanu, Guillaume Dujardin +2
We consider the Gross-Pitaevskii equation with a confining ring potential with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we numerically highlight the n…
math.NA2024
Finite volumes for the Gross-Pitaevskii equation
Quentin Chauleur
We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux app…