Soliton dynamics in the Ostrovsky equation with anomalous dispersion

TL;DR

This paper explores soliton formation, interaction, and recurrence phenomena in the non-integrable Ostrovsky equation with anomalous dispersion, revealing inelastic interactions and the emergence of dominant solitons in bounded systems.

Contribution

It provides new insights into soliton dynamics in the Ostrovsky equation, including the existence of zero-mass solitons and their complex interactions, which were not previously characterized.

Findings

Zero-mass solitons can form from pulse-like initial conditions.

Soliton interactions are inelastic, leading to a dominant 'soliton-champion'.

Recurrence phenomena differ from those in the KdV equation.

Abstract

We investigate the formation and interaction of solitons in the non-integrable Ostrovsky equation characterized by anomalous (positive) dispersion. This equation is relevant for describing wave phenomena in various media, including plasma, solids, and optical fibers. Our findings indicate that certain Ostrovsky solitons, which possess zero total ''mass'' and exhibit non-monotonic asymptotic behavior, can arise from initial perturbations of a pulse-like nature. These solitons may organize into regular trains, where they are arranged according to their amplitude, or they may form irregular, nonstationary configurations of bound interacting solitons, or even multi-soliton structures. Furthermore, we demonstrate that the interactions between solitons in the Ostrovsky equation are inelastic, resulting in the emergence of a dominant soliton, or ''soliton-champion,'' within closed systems, such as those with periodic boundary conditions. In such systems, the soliton with the highest amplitude acts as a ''terminator,'' annihilating smaller amplitude solitons and absorbing a portion of their energy. We also analyze the recurrence phenomenon and determine that, although it resembles that of the Korteweg-de Vries equation, it exhibits distinct features.