Three-way focusing Zakharov-Shabat systems with zero diagonal entry

Demontis, Francesco

;van der Mee, Cornelis

2025-01-01

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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.