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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2026,6,15]]},"abstract":"<jats:p>This paper deals with the traveling wave solutions in the one-dimensional Euler\u2013Poisson system equipped with the Boltzmann relation. By applying the method of dynamical systems to analyze the corresponding traveling wave system and find its phase portraits, we investigate the traveling wave solutions of the system without any restrictions. Under given parameter conditions, the existence of periodic wave solution families, compacton solution families, solitary wave solutions, kink wave solutions and anti-kink wave solutions is proved for the system with three variables. Our results complement the results in [ Bae et al. ,\u00a0 2025 ] and demonstrate that the system cannot have peakon solutions.<\/jats:p>","DOI":"10.1142\/s0218127426500896","type":"journal-article","created":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T05:43:09Z","timestamp":1771220589000},"source":"Crossref","is-referenced-by-count":0,"title":["Existence of Periodic Waves and Compacton Solutions of the Euler\u2013Poisson Equation: A Dynamical System Approach"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1627-0035","authenticated-orcid":false,"given":"Junmin","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, P. R. 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