@article{10902/38144,
year = {2025},
month = {11},
url = {https://hdl.handle.net/10902/38144},
abstract = {The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field. First, using bifurcation theory, we can rigorously prove the existence of periodic traveling waves of small amplitude. Furthermore, our analysis also evidences the existence of different type of traveling waves. To this end, we present a second approach based on the analysis of the differential system satisfied by the traveling wave profiles, the existence of equilibria, and the identification of associated homoclinic and periodic orbits around them. The study makes use of linearization techniques, normal forms, and numerical computations to show the existence of different types of traveling wave solutions, with monotone and non-monotone behavior and different regularity, as well as periodic traveling waves.},
organization = {The authors gratefully acknowledge Claudia García for fruitful discussions regarding bifurcation theory and Daniel Sánchez-Simón del Pino for pointing out the reference of Lemma 2.1. D.A-O has been partially supported by RYC2023-045563-I (MICIU/AEI/10.13039/501100011033 and FSE+) and the project PID2023-148028NB-100. D.AO and R. G-B are also supported by the project ‘‘Análisis Matemático Aplicado 𝑦 Ecuaciones Diferenciales’’ Grant PID2022-141187NB-I00 funded by MCIN/AEI and acronym ‘‘AMAED’’. This paper is part of the project PID2022-141187NB-I00 with acronym AMAED funded by MICIU/AEI/10.13039/501100011033 and by FEDER, UE/AEI/10.13039/501100011033/FEDER, UE. A.D. is supported by the Spanish Agencia Estatal de Investigación under Research Grant PID2023-147073NB100.},
publisher = {Elsevier},
publisher = {Physica D: Nonlinear Phenomena, 2025, 481, 134803},
title = {On the existence of traveling wave solutions for cold plasmas},
author = {Alonso-Orán, Diego and Durán, Angel and Granero Belinchón, Rafael},
}