From the AKNS system to the matrix Schroedinger equation with vanishing potentials: Direct and inverse problems

2021/09/23 by Francesco Demontis, Cornelis van der Mee, Demontis, Francesco +1 · 1 citation
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2109.11684

Abstract

We relate the scattering theory of the focusing AKNS system with vanishing boundary conditions to that of the matrix Schroedinger equation. The corresponding Miura transformation which allows this connection, converts the focusing matrix nonlinear Schroedinger (NLS) equation into a new nonlocal integrable equation. We apply the matrix triplet method to derive the multisoliton solutions of the nonlocal integrable equation, thus proposing a new method to solve the matrix NLS equation.

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• Uniform stability for the matrix inverse Sturm-Liouville problems

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