By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer–Lund–Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed.

Nonlocal integrable PDEs from hierarchies of symmetry laws: The example of Pohlmeyer–Lund–Regge equation and its reflectionless potential solutions

F. Demontis;ORTENZI, GIOVANNI
;
C. van der Mee
2018

Abstract

By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer–Lund–Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed.
bi-Hamiltonian pencil; Integrable systems; Hierarchies of commuting flows; Nonlocal PDEs; Inverse scattering method
File in questo prodotto:
File Dimensione Formato  
LundRegge-postReferaggio.pdf

Solo gestori archivio

Tipologia: versione post-print
Dimensione 3.66 MB
Formato Adobe PDF
3.66 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/11584/242601
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact