par Kozyreff, Gregory 
Référence 2024 SIAM Conference on Nonlinear Waves and Coherent Structures (24-27 June 2024: Baltimore, USA)
Publication Non publié, 2024-06-25
Référence 2024 SIAM Conference on Nonlinear Waves and Coherent Structures (24-27 June 2024: Baltimore, USA)
Publication Non publié, 2024-06-25
Communication à un colloque
| Résumé : | We carry out the multiple-scale derivation of the NLS equation up to arbitrary order for a general class of wave equations. When the group and phase velocities are exponentially close to each other, we show that the soliton dynamics completely departs from what the NLS equation predicts. The shape of the fundamental soliton, whether bright or dark, remains as in the textbook picture. However, the motion is now governed by the exponentially weak interaction between the wave envelope and the carrier wave. This interplay results in a finite locking range in which the velocity of the wave packet is not constant but always oscillates around an average value. The average speed of the soliton is the phase velocity instead of the group velocity. We provide an intuitive reason for this phenomenon as well as an analysis based on Stokes phenomenon beyond all orders of the multiple-scale expansion.Eventually, a new equation of motion is derived in the vicinity of the locking range. In a frame that moves at the phase velocity, it turns out to be equivalent to that of a pendulum. The generality of the derivation suggests that the conclusions apply generically to weakly nonlinear wave packets in dispersive systems that admit equality of group and phase velocities at a certain wavelength. |
