Matrix Zakharov-Shabat Systems with Zero Diagonal Entry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918209436778496 |
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| author | van der Mee, Cornelis |
| author_facet | van der Mee, Cornelis |
| contents | In this article we develop the direct and inverse scattering theory of the Ablowitz-Kaup-Newell-Segur (AKNS) system $\bv_x=(ik\zS+\CQ(x))\bv$, where $\zS$ is a diagonal $n\times n$ matrix with diagonal entries $1$ and $-1$ and a single zero diagonal entry and $\CQ(x)$ is an $n\times n$ potential anticommuting with $\zS$ with entries in $L^1(\R)$. 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 system of long-wave-short-wave equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix Zakharov-Shabat Systems with Zero Diagonal Entry van der Mee, Cornelis Functional Analysis 34A55, 34L25 In this article we develop the direct and inverse scattering theory of the Ablowitz-Kaup-Newell-Segur (AKNS) system $\bv_x=(ik\zS+\CQ(x))\bv$, where $\zS$ is a diagonal $n\times n$ matrix with diagonal entries $1$ and $-1$ and a single zero diagonal entry and $\CQ(x)$ is an $n\times n$ potential anticommuting with $\zS$ with entries in $L^1(\R)$. 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 system of long-wave-short-wave equations. |
| title | Matrix Zakharov-Shabat Systems with Zero Diagonal Entry |
| topic | Functional Analysis 34A55, 34L25 |
| url | https://arxiv.org/abs/2511.15348 |