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arXiv · 1004.5355

On Darboux-Treibich-Verdier potentials

A. P. Veselov
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Abstract

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-ω_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.

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A. P. Veselov. 2010-04-29. On Darboux-Treibich-Verdier potentials. https://doi.org/10.1007/s11005-010-0420-6

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