AI Article Synopsis
- The study investigates how universal the Fermi-Pasta-Ulam recurrence is in the context of multisoliton fission using the semiclassical defocusing nonlinear Schrödinger equation, which describes nonlinear wave behavior in various systems.
- It employs a Wentzel-Kramers-Brillouin approach to predict soliton-like excitations' characteristics after breaking, including their number, amplitude, and velocity based on a dispersion parameter.
- The findings highlight a universal mechanism similar to that in the Korteweg-deVries equation but also point out significant differences due to distinct scaling rules for soliton velocities between the two models.
Article Abstract
We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analyzing the case of the semiclassical defocusing nonlinear Schrödinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in a fully analytical way, the number and the features (amplitude and velocity) of solitonlike excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits us to predict and analyze the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation. We show, however, that important differences exist between the two models, arising from the different scaling rules obeyed by the soliton velocities.
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