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Article Dans Une Revue Journal of Nonlinear Science Année : 2024

Numerical computation of dark solitons of a nonlocal nonlinear Schrödinger equation

Résumé

The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been established recently [10]. Mathematically, these solitons correspond to minimizers of the energy at fixed momentum and are orbitally stable. This paper provides a numerical method to compute approximations of such solitons for these types of equations, and provides actual numerical experiments for several types of physically relevant nonlocal potentials. These simulations allow us to obtain a variety of dark solitons, and to comment on their shapes in terms of the parameters of the nonlocal potential. In particular, they suggest that, given the dispersion relation, the speed of sound and the Landau speed are important values to understand the properties of these dark solitons. They also allow us to test the necessity of some sufficient conditions in the theoretical result proving existence of the dark solitons.
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Dates et versions

hal-04058467 , version 1 (04-04-2023)
hal-04058467 , version 2 (02-05-2023)

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André de Laire, Guillaume Dujardin, Salvador López-Martínez. Numerical computation of dark solitons of a nonlocal nonlinear Schrödinger equation. Journal of Nonlinear Science, 2024, 34 (1), ⟨10.1007/s00332-023-10001-7⟩. ⟨hal-04058467v2⟩
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