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arXiv · 2502.04707

NLS approximation and dark solitons for the Adlam-Allen model of cold collisionless plasmas

George P. Veldes·Vassilis Koukouloyannis·Dimitrios J. Frantzeskakis·Panayotis G. Kevrekidis
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Abstract

The present work extends earlier considerations on a quintessential model of cold, collisionless plasmas, namely the Adlam-Allen model. Previously, an analysis of homoclinic solutions around a non-vanishing background (associated with a saddle equilibrium) led to a Korteweg-de Vries reduction. Here, we consider a different equilibrium of the co-traveling frame model, namely a center, and expanding around it, by means of a multiple-scale methodology and suitable scalings, leads to an effective defocusing nonlinear Schr{ö}dinger equation. Leveraging the latter, we construct, for the first time to our knowledge, physically realistic dark soliton waveforms of the Adlam-Allen model. We subsequently test the numerical evolution of such coherent structures, identifying them as long-lived waveforms of the full model.

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George P. Veldes, Vassilis Koukouloyannis, Dimitrios J. Frantzeskakis, Panayotis G. Kevrekidis. 2025-04-22. NLS approximation and dark solitons for the Adlam-Allen model of cold collisionless plasmas. https://arxiv.org/abs/2502.04707

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