A systematic approach to the study of nonlinear evolution equations based on the theory of the equivalence transformations is suggested. In this paper it is applied to the Burgers and to the Korteweg-de Vries equations. The main result is that the Hopf-Cole transformation for the Burgers equation and the Miura, Bäcklund, and Hirota transformations for the Korteweg-de Vries equation (together with the linear equations of the inverse scattering theory) are all deduced from a single general equivalence condition. Copyright © 1977 American Institute of Physics.

Magri, F. (1977). Equivalence transformations for nonlinear evolution equations. JOURNAL OF MATHEMATICAL PHYSICS, 18(7), 1405-1411 [10.1063/1.523437].

Equivalence transformations for nonlinear evolution equations

MAGRI, FRANCO
1977

Abstract

A systematic approach to the study of nonlinear evolution equations based on the theory of the equivalence transformations is suggested. In this paper it is applied to the Burgers and to the Korteweg-de Vries equations. The main result is that the Hopf-Cole transformation for the Burgers equation and the Miura, Bäcklund, and Hirota transformations for the Korteweg-de Vries equation (together with the linear equations of the inverse scattering theory) are all deduced from a single general equivalence condition. Copyright © 1977 American Institute of Physics.
Articolo in rivista - Articolo scientifico
Nonlinear evolution equations
English
1405
1411
Magri, F. (1977). Equivalence transformations for nonlinear evolution equations. JOURNAL OF MATHEMATICAL PHYSICS, 18(7), 1405-1411 [10.1063/1.523437].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/10281/18493
Citazioni
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 18
Social impact