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BIRS Workshop Lecture Videos

Asymptotics and solitons for defocusing nonlocal nonlinear Schrdinger equations Dimitri, Frantzeskakis


Asymptotic reductions of a defocusing nonlocal nonlinear Schrdinger model in (2+1)-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then far-field, KadomtsevPetviashvilli I and II (KP-I, KP- II) equations for right- and left-going waves are found. This way, small-amplitude, planar or ring-shaped, dark or anti-dark solitons are derived, whose nature and stability is determined by a parameter defined by the physical parameters of the original nonlocal system. It is shown that (dark) anti-dark solitons are supported by a weak (strong) nonlocality, and are unstable (stable) against transverse perturbations. The analytical predictions are corroborated by direct numerical simulations.

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