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

Volume 12, Issue 12, pp 846--855
Publication Date: August 07, 2019 Submission Date: April 20, 2019 Revision Date: May 23, 2019 Accteptance Date: June 02, 2019
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### Authors

Mohammed Abobaker - Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics, St. Petersburg Polytechnic University, Russia.

### Abstract

In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gas-dust 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.

### Share and Cite

##### ISRP Style

Mohammed Abobaker, 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, 12 (2019), no. 12, 846--855

##### AMA Style

Abobaker Mohammed, Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud. J. Nonlinear Sci. Appl. (2019); 12(12):846--855

##### Chicago/Turabian Style

Abobaker, Mohammed. "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, 12, no. 12 (2019): 846--855

### Keywords

• Hydrodynamics
• non-linear PDE
• Cole-Hopf method
• gravitating system gas-dust cloud

•  35Q85
•  85A05

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