Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud

Journal of Nonlinear Sciences and Applications Pub Date : 2019-08-07 DOI:10.22436/JNSA.012.12.06

M. Abobaker

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.

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应用Cole-Hopf变换求球形气尘云引力系统动力学解析解

本文给出了自重力球形对称气尘云一维动力学的一个简单模型。我们考虑密度和速度的两个特殊初始条件。本文采用解析式Cole-Hopf变换方法研究了气尘云引力系统的动力学。在此基础上，应用特征化方法将偏微分方程简化为完全可解的常微分方程组。本研究得到的结果用图形表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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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.