Optimal Classification of Lie Sub-Algebras and Self-Similar Solution Using Group Invariance Method for Shock Wave in Self-Gravitating Ideal Gas with Magnetic Field and Variable Density in Rotating Medium: Isothermal Flow

Key Points

• Shock wave behavior significantly depends on the classification of lie sub-algebras, revealing complex interactions.
• The study found that applying the group invariance method enhances solution accuracy in varying densities of self-gravitating ideal gas.
• Analysis using group invariance method outlines the impact of magnetic fields in isothermal flow under rotating conditions.
• This framework highlights the importance of established classifications for advancing theoretical physics.