Equilibrium of Charges and Differential Equations Solved by Polynomials II
Abstract
The study establishes the relationship between the equilibria of two species of vortices with a circulation ratio of -2 and the factorization/Darboux transformation of the Schrödinger operator.
We continue study of equilibrium of two species of 2d coulomb charges (or point vortices in 2d ideal fluid) started in Lv. Although for two species of vortices with circulation ratio -1 the relationship between the equilibria and the factorization/Darboux transformation of the Schrodinger operator was established a long ago, the question about similar relationship for the ratio -2 remained unanswered. Here we present the answer.
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