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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.21441 |
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| _version_ | 1866917169426595840 |
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| author | Dragović, Vladimir Shramchenko, Vasilisa |
| author_facet | Dragović, Vladimir Shramchenko, Vasilisa |
| contents | We introduce the dynamics of Toda curves of order $N$ and derive differential equations governing this dynamics. We apply the obtained results to describe isoperiodic deformations of $N$-periodic Toda chains and periodic difference Korteweg-de Vries equation. We describe deformations of the essential spectra of $N$-periodic two-sided Jacobi matrices. We also study singular regimes of $SU(N)$ Seiberg-Witten theory and describe their deformations preserving the number of singularities where new massless particles may occur. We introduce and describe isoequilibrium deformations of arbitrary collections of $d$ real disjoint closed intervals. We conclude by providing explicit triangular solutions to constrained Schlesinger systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isoperiodic deformations of Toda curves and chains, the difference Korteweg - de Vries equation, and $SU(N)$ Seiberg-Witten theories Dragović, Vladimir Shramchenko, Vasilisa Algebraic Geometry Mathematical Physics Analysis of PDEs Exactly Solvable and Integrable Systems We introduce the dynamics of Toda curves of order $N$ and derive differential equations governing this dynamics. We apply the obtained results to describe isoperiodic deformations of $N$-periodic Toda chains and periodic difference Korteweg-de Vries equation. We describe deformations of the essential spectra of $N$-periodic two-sided Jacobi matrices. We also study singular regimes of $SU(N)$ Seiberg-Witten theory and describe their deformations preserving the number of singularities where new massless particles may occur. We introduce and describe isoequilibrium deformations of arbitrary collections of $d$ real disjoint closed intervals. We conclude by providing explicit triangular solutions to constrained Schlesinger systems. |
| title | Isoperiodic deformations of Toda curves and chains, the difference Korteweg - de Vries equation, and $SU(N)$ Seiberg-Witten theories |
| topic | Algebraic Geometry Mathematical Physics Analysis of PDEs Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.21441 |