TY - JOUR AU - Abobaker, Mohammed PY - 2019 TI - Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud JO - Journal of Nonlinear Sciences and Applications SP - 846--855 VL - 12 IS - 12 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.012.12.06 DO - 10.22436/jnsa.012.12.06 ID - Abobaker2019 ER -