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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.20536 |
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| _version_ | 1866916968117829632 |
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| author | Rubbioni, Paola Sambucini, Anna Rita Zampogni, Luca |
| author_facet | Rubbioni, Paola Sambucini, Anna Rita Zampogni, Luca |
| contents | The goal of the present paper is that of defining the so-called Sturm-Liouville hierarchy of evolution equations, firstly by using the zero-curvature formalism, then by using the asymptotic properties of the Weyl $m$-functions for certain classes of pairs $(q,y)$ of the Sturm-Liouville eigenvalue equation $$-φ''+qφ=λyφ,$$ in the space $L^2(\mathbb R,ydx)$. Since the Weyl $m$-functions are known to contain all the information concerning the spectral properties of the above equation, the determination of the evolution of some spectral characteristics will allow to determine solutions of the hierarchies of evolution equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Sturm-Liouville Hierarchy of evolution equations and the Weyl functions of related spectral problems Rubbioni, Paola Sambucini, Anna Rita Zampogni, Luca Classical Analysis and ODEs The goal of the present paper is that of defining the so-called Sturm-Liouville hierarchy of evolution equations, firstly by using the zero-curvature formalism, then by using the asymptotic properties of the Weyl $m$-functions for certain classes of pairs $(q,y)$ of the Sturm-Liouville eigenvalue equation $$-φ''+qφ=λyφ,$$ in the space $L^2(\mathbb R,ydx)$. Since the Weyl $m$-functions are known to contain all the information concerning the spectral properties of the above equation, the determination of the evolution of some spectral characteristics will allow to determine solutions of the hierarchies of evolution equations. |
| title | The Sturm-Liouville Hierarchy of evolution equations and the Weyl functions of related spectral problems |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.20536 |