Soliton dynamics in random fields: The Benjamin-Ono equation framework

TL;DR

This paper studies how algebraic solitons governed by the Benjamin-Ono equation interact with random forces, revealing regimes of splitting, recombination, and variable speeds, with theoretical and numerical agreement.

Contribution

It introduces a framework for analyzing soliton interactions with random forces using the Benjamin-Ono equation, identifying new dynamic regimes and asymptotic behaviors.

Findings

Averaged soliton field splits into two steady pulses.

Regimes where solitons travel in opposite directions.

Periodic soliton splitting and recombination observed.

Abstract

Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated using the Benjamin-Ono equation. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly distributed, while its frequency spectrum has a Gaussian shape centered at a peak frequency. The expected value of the averaged soliton wave field is computed asymptotically and compared with numerical results, showing strong agreement. We identify parameter regimes where the averaged soliton field splits into two steady pulses and a regime where the soliton field splits into two solitons traveling in opposite directions. In the latter case, the averaged soliton speeds are variable. In both scenarios, the soliton field is damped by the external force. Additionally, we identify a regime where the averaged soliton exhibits the following behavior: it splits into two distinct solitons and then recombines to form a single soliton. This motion is periodic over time.