Dispersion of three-dimensional oscillons: a standing-wave perspective
Abstract
A spherically symmetric standing wave confined within a finite-radius ball, with weak radiative exchange between its core and boundary, provides a model for an intermediate stage in the adiabatic evolution of the ϕ4 oscillon. We employ a multiscale variational framework to derive an approximate description of these standing waves and their energy-frequency relation. The resulting dispersion curve is compared with that obtained from numerical solutions of the boundary value problem for the ϕ4 equation on a two dimensional (time and radius) domain. The agreement between the numerical and variational results is excellent near the endpoint of the continuous spectrum but deteriorates as ω is reduced below 0.85 ω0. We attribute this discrepancy to the growth of the radiation wing, which is neglected in the variational ansatz.
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BibTeX
@misc{barashenkov2026dispersion,
title = {{Dispersion of three-dimensional oscillons: a standing-wave perspective}},
author = {I. V. Barashenkov and R. De Sousa and N. V. Alexeeva and A. Dika and E. V. Zemlyanaya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26281},
eprint = {2610.26281},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26281},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dispersion of three-dimensional oscillons: a standing-wave perspective
AU - I. V. Barashenkov
AU - R. De Sousa
AU - N. V. Alexeeva
AU - A. Dika
AU - E. V. Zemlyanaya
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26281
UR - https://arxiv.org/abs/2610.26281
AB - A spherically symmetric standing wave confined within a finite-radius ball, with weak radiative exchange between its core and boundary, provides a model for an intermediate stage in the adiabatic evolution of the ϕ^4 oscillon. We employ a multiscale variational framework to derive an approximate description of these standing waves and their energy-frequency relation. The resulting dispersion curve is compared with that obtained from numerical solutions of the boundary value problem for the ϕ^4 equation on a two dimensional (time and radius) domain. The agreement between the numerical and variational results is excellent near the endpoint of the continuous spectrum but deteriorates as ω is reduced below 0.85 ω_0. We attribute this discrepancy to the growth of the radiation wing, which is neglected in the variational ansatz.
ER -