{"title":"Long-Wavelength Limit of a Quantum Euler–Poisson System in the (3+1) Dimensions for a Dense Magnetoplasma","authors":"Rong Rong, Xueke Pu","doi":"10.1111/sapm.70064","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This paper presents the derivation of a (3+1)-dimensional quantum Zakharov–Kuznetsov (QZK) equation for ion acoustic waves. Using a singular perturbation method within the long-wavelength limit of the (3+1)-dimensional quantum Euler–Poisson system, we demonstrate that the QZK equation can be systematically derived through the Gardner–Morikawa transformation. The derived equation is valid over a time interval of order <span></span><math>\n <semantics>\n <mrow>\n <mi>O</mi>\n <mo>(</mo>\n <msup>\n <mi>ε</mi>\n <mrow>\n <mo>−</mo>\n <mn>3</mn>\n <mo>/</mo>\n <mn>2</mn>\n </mrow>\n </msup>\n <mo>)</mo>\n </mrow>\n <annotation>$O(\\varepsilon ^{-3/2})$</annotation>\n </semantics></math>.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 5","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.70064","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents the derivation of a (3+1)-dimensional quantum Zakharov–Kuznetsov (QZK) equation for ion acoustic waves. Using a singular perturbation method within the long-wavelength limit of the (3+1)-dimensional quantum Euler–Poisson system, we demonstrate that the QZK equation can be systematically derived through the Gardner–Morikawa transformation. The derived equation is valid over a time interval of order .
期刊介绍:
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.