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On Darboux–Treibich–Verdier Potentials

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Abstract

It is shown that the four-parameter family of elliptic functions

$$ u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i) $$

introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, generates the most general linear subspace of meromorphic functions containing infinitely many finite-gap potentials.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

    Alexander P. Veselov

  2. Moscow State University, Moscow, 119899, Russia

    Alexander P. Veselov

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  1. Alexander P. Veselov
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Correspondence to Alexander P. Veselov.

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To V. B. Matveev on his 65th birthday

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Veselov, A.P. On Darboux–Treibich–Verdier Potentials. Lett Math Phys 96, 209–216 (2011). https://doi.org/10.1007/s11005-010-0420-6

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  • DOI: https://doi.org/10.1007/s11005-010-0420-6

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