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This is a Quantitative Study study.

October 9, 2025Open Access

Transverse asymptotic stability of line solitary waves for the Ionic Euler-Poisson system

Key Points

The study confirms the asymptotic stability of solitary waves in the Ionic Euler-Poisson system when perturbed.
It finds that small localized perturbations lead to robust global smooth solutions in one-dimensional solitary wave dynamics.
The approach entails proving both linear and nonlinear stability properties under specific conditions of ion dynamics.
These results may enable further exploration into the behavior of solitary waves in plasma physics and related fields.

Abstract

We prove the linear and nonlinear asymptotic stability of small amplitude one-dimensional solitary waves submitted to small localized irrotational perturbations in the three dimensional Euler-Poisson system describing the dynamics of ions. In particular, in this regime, we obtain the existence of global smooth solutions and describe their asymptotic behavior.

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Cite This Study

Rousset et al. (Thu,) studied this question.

synapsesocial.com/papers/68e7103b90569dd607ee692d https://doi.org/https://doi.org/10.48550/arxiv.2507.23572