Soliton dynamics in the Gardner-Ostrovsky equation
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.
Related
- An Extended 2+1-Dimensional Gardner Equation: On Moving Boundary Problems Solvable via Ermakov-Painlevé II Symmetry Reduction
- Deep Learning of Hirota τ-Function for Soliton Solutions of a (3+1)-Dimensional Nonlocal Evolution Equation
- Physics-informed neural networks for soliton solutions and parameter identification of the two-mode Korteweg–de Vries equation
- NJL-Chiral Soliton and the Nucleon Equation of State at supra-saturation density: Impact of Chiral Symmetry Restoration
- The \texorpdfstring{N-soliton}{N-soliton} solution formula for the Kaup--Kupershmidt equation
BibTeX
@misc{fariello2026soliton,
title = {{Soliton dynamics in the Gardner-Ostrovsky equation}},
author = {R. Fariello and M. S. Soares and Y. A. Stepanyants},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05468},
eprint = {2610.05468},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05468},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Soliton dynamics in the Gardner-Ostrovsky equation
AU - R. Fariello
AU - M. S. Soares
AU - Y. A. Stepanyants
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05468
UR - https://arxiv.org/abs/2610.05468
AB - 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.
ER -