Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie

  • Danilo García Hernández IMEC-UNICAMP, Escola de matemática, Campinas, Brasil.
  • Oscar Mario Londoño Duque IMEC-UNICAMP, Escola de matemática, Campinas, Brasil.
  • Yeisson Acevedo Universidad EAFIT, Departamento de ciencias matemáticas, Medellín, Colombia.
  • Gabriel Loaiza Universidad EAFIT, Departamento de ciencias matemáticas, Medellín, Colombia.

Resumen

Obtenemos la clasificación completa del grupo de simetría de Lie y los operadores generadores del sistema optimal asociados a un caso particular de la ecuación de Kummer - Schwarz generalizada. Utilizando esos operadores, caracterizamos todas las soluciones invariantes, se encontraron soluciones alternativas para la ecuación estudiada y se clasifica el álgebra de Lie asociada al grupo de simetría.

Palabras clave: Soluciones invariantes, grupo de simetría de Lie, Sistema optimal, Clasificación del álgebra de Lie, Ecuación de Kummer - Schwarz

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Publicado
2021-10-08