Symmetric Algebras and Normal Forms of Third Order Ordinary Differential Equations

Key Points

• The research aims to classify third order ordinary differential equations based on their symmetry algebra and structure.
• Classify third order ordinary differential equations according to the dimension of their symmetry algebras.
• Establish canonical forms for generators and representatives of these equations with specific symmetry counts.
• Investigate equations possessing 4 to 7 independent symmetries.
• Canonical forms for generators of third order ordinary differential equations with 4, 5, 6, or 7 independent symmetries were established.
• These classifications provide insights into the structure of symmetry algebras corresponding to these equations.