In this article we develop the direct and inverse scattering theory of the AKNS system Vx=(ikΣ+Q(x))V, where Σ=diag(1,0,-1) and Q(x) is an off-diagonal 3×3σ-focusing potential with entries in L1(R). We derive the time evolution of the scattering data which, through the inverse scattering transform, lead to the solution of the initial-value problem for a generalized long-wave-short-wave equation. We determine the essential spectrum of the AKNS system rigorously.
Three-way focusing Zakharov-Shabat systems with zero diagonal entry
Demontis, Francesco
;van der Mee, Cornelis
2025-01-01
Abstract
In this article we develop the direct and inverse scattering theory of the AKNS system Vx=(ikΣ+Q(x))V, where Σ=diag(1,0,-1) and Q(x) is an off-diagonal 3×3σ-focusing potential with entries in L1(R). We derive the time evolution of the scattering data which, through the inverse scattering transform, lead to the solution of the initial-value problem for a generalized long-wave-short-wave equation. We determine the essential spectrum of the AKNS system rigorously.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
RicercheMatematica2025Pubblicato.pdf
accesso aperto
Tipologia:
versione editoriale (VoR)
Dimensione
455.5 kB
Formato
Adobe PDF
|
455.5 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
