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arXiv · 2610.05468

Soliton dynamics in the Gardner-Ostrovsky equation

R. Fariello·M. S. Soares·Y. A. Stepanyants
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Abstract

We investigate soliton formation and interactions in the non-integrable Gardner-Ostrovsky equation (alias the rotation-modified Gardner equation) with anomalous (positive) dispersion. This equation is relevant to the description of wave dynamics in plasmas and other dispersive media. We show that a special class of solitons, characterized by zero total mass and non-monotonic asymptotics, can emerge from pulse-like initial perturbations. Depending on the initial conditions, these solitons may form regular amplitude-ordered trains, irregular nonstationary ensembles of interacting localized structures, or stationary propagating multi-soliton complexes. We further demonstrate that soliton interactions in the Gardner-Ostrovsky equation are inherently inelastic, leading to the emergence of a dominant "soliton-champion" in closed systems. For example, under periodic boundary conditions, only the largest-amplitude soliton ultimately survives, while all smaller solitons are gradually eliminated through successive interactions. Despite their inelastic interactions, Gardner-Ostrovsky solitons exhibit remarkable robustness.

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R. Fariello, M. S. Soares, Y. A. Stepanyants. 2026-10-04. Soliton dynamics in the Gardner-Ostrovsky equation. https://arxiv.org/abs/2610.05468

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