{"title":"Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud","authors":"M. Abobaker","doi":"10.22436/JNSA.012.12.06","DOIUrl":null,"url":null,"abstract":"In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gasdust cloud. We consider two special initial conditions for density and velocity. We take an analytical Cole-Hopf transformation method to study the dynamics of a gravitating system of a gas-dust cloud. The technique is employed to simplify the equations of dynamics, and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The obtained results in this study are presented in graphics.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.012.12.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gasdust cloud. We consider two special initial conditions for density and velocity. We take an analytical Cole-Hopf transformation method to study the dynamics of a gravitating system of a gas-dust cloud. The technique is employed to simplify the equations of dynamics, and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The obtained results in this study are presented in graphics.
期刊介绍：
The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.
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