On Darboux-Treibich-Verdier potentials

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, is the most general meromorphic family containing infinitely many finite-gap potentials.

8 pages

References in corpus (1)

• On the rational monodromy-free potentials with sextic growth

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