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Stokes phenomenon in the propagation of weakly nonlinear wave packets

par Kozyreff, Gregory
Référence IsaacNewton Institute Workshop on Mathematics of beyond all-orders phenomena (31 October - 4 November 2022: Cambridge, UK)
Publication Non publié, 2022-10-31

Communication à un colloque

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Résumé :

The universal theory of weakly nonlinear wave packets given by the nonlinear Schrodinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple scale analysis carried out beyond all orders reveals that a single soliton, bright or dark, can travel at a different speed than the group velocity. In an exponentially small but finite range of parameters, the envelope of the soliton is locked to the rapid oscillations of the carrier wave. Eventually, the dynamics is governed by an equation anologous to that of a pendulum, in which the center of mass of the soliton is subjected to a periodic potential. Consequently, the soliton speed is not constant and generally contains a periodic component.