We relate the scattering theory of the focusing AKNS system with equally sized nonvanishing boundary conditions to that of the matrix Schrodinger equation. This (shifted) Miura transformation converts the focusing matrix nonlinear Schrodinger (NLS) equation into a new nonlocal integrable equation. We apply the matrix triplet method of solving the Marchenko integral equations by separation of variables to derive the multisoliton solutions of this nonlocal equation, thus proposing a method to solve the reflectionless matrix NLS equation.

A Matrix Schrodinger Approach to Focusing Nonlinear Schrodinger Equations with Nonvanishing Boundary Conditions

Demontis, F
;
van der Mee, C
2022-01-01

Abstract

We relate the scattering theory of the focusing AKNS system with equally sized nonvanishing boundary conditions to that of the matrix Schrodinger equation. This (shifted) Miura transformation converts the focusing matrix nonlinear Schrodinger (NLS) equation into a new nonlocal integrable equation. We apply the matrix triplet method of solving the Marchenko integral equations by separation of variables to derive the multisoliton solutions of this nonlocal equation, thus proposing a method to solve the reflectionless matrix NLS equation.
Miura transformation
Matrix KdV equation
Matrix NLS equation
Matrix triplet method
Integrable nonlocal equation
File in questo prodotto:
File Dimensione Formato  
NewApproachNonVanishing.pdf

Solo gestori archivio

Tipologia: versione editoriale
Dimensione 539.73 kB
Formato Adobe PDF
539.73 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Nonvanishing200522_final.pdf

embargo fino al 12/06/2023

Descrizione: accepted version
Tipologia: altro documento allegato
Dimensione 1.04 MB
Formato Adobe PDF
1.04 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: https://hdl.handle.net/11584/349036
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact