In the recent literature, several equations have been studied with purported new approaches because the authors claim that these equations were not amenable to exact treatment using known methods. But we show that all these equations have sufficient Lie point symmetries to make them integrable by quadrature, if not linearizable. When one gets a “miraculous haul of fishes,” namely, exact methods of solution, first integrals, even linearization, then Lie symmetries shall be found. Lie group analysis was and should still be considered an essential tool for anyone who wants to solve equations of relevance in physics and other scientific fields.

Let's Lie: a miraculous haul of fishes

NUCCI, Maria Clara
2005-01-01

Abstract

In the recent literature, several equations have been studied with purported new approaches because the authors claim that these equations were not amenable to exact treatment using known methods. But we show that all these equations have sufficient Lie point symmetries to make them integrable by quadrature, if not linearizable. When one gets a “miraculous haul of fishes,” namely, exact methods of solution, first integrals, even linearization, then Lie symmetries shall be found. Lie group analysis was and should still be considered an essential tool for anyone who wants to solve equations of relevance in physics and other scientific fields.
2005
File in questo prodotto:
File Dimensione Formato  
3213751.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 153.13 kB
Formato Adobe PDF
153.13 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3213751
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact