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arXiv · 2512.21441

Isoperiodic deformations of Toda curves and chains, the difference Korteweg - de Vries equation, and $SU(N)$ Seiberg-Witten theories

Vladimir Dragović·Vasilisa Shramchenko
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Abstract

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.

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Vladimir Dragović, Vasilisa Shramchenko. 2025-12-24. Isoperiodic deformations of Toda curves and chains, the difference Korteweg - de Vries equation, and $SU(N)$ Seiberg-Witten theories. https://arxiv.org/abs/2512.21441

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