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arXiv · 2610.26281

Dispersion of three-dimensional oscillons: a standing-wave perspective

I. V. Barashenkov·R. De Sousa·N. V. Alexeeva·A. Dika·E. V. Zemlyanaya
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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 $ϕ^4$ 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.

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I. V. Barashenkov, R. De Sousa, N. V. Alexeeva, A. Dika, E. V. Zemlyanaya. 2026-10-19. Dispersion of three-dimensional oscillons: a standing-wave perspective. https://arxiv.org/abs/2610.26281

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