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<p>The Emden–Fowler equation is a fundamental model in various fields of physics. In this work, we generalize this equation and conduct a thorough investigation of its symmetries and dynamical properties. Our results include a complete classification of the symmetry group, the derivation of the Lagrangian and conservation laws, and the computation of invariant solutions. By combining global and local analysis, we provide a comprehensive understanding of the dynamics of the reduced equations.</p>

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Study of the Emden–Fowler differential equation by complete classification of symmetry groups and dynamical analysis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月22日

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  • Germán F. Escobar F.,
  • Oscar M. Londoño D.,
  • Sebastian Nuñez T.,
  • Kevyn A. Cuenca E.

摘要

The Emden–Fowler equation is a fundamental model in various fields of physics. In this work, we generalize this equation and conduct a thorough investigation of its symmetries and dynamical properties. Our results include a complete classification of the symmetry group, the derivation of the Lagrangian and conservation laws, and the computation of invariant solutions. By combining global and local analysis, we provide a comprehensive understanding of the dynamics of the reduced equations.