On Darboux-Treibich-Verdier potentials

Details On Darboux-Treibich-Verdier potentials On Darboux-Treibich-Verdier potentials

2010-04-29

arxiv.org/abs/1004.5355v1

Physics

Mathematical Physics

8 pages

Scientific paper

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.

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