Abstract
Abstract We continue study of equilibrium of two species of 2d coulomb charges (or point vortices in 2d ideal fluid) started in [20]. 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: One has to consider Darboux-type transformations of third order differential operators rather than second order Schrodinger operators. Furthermore, we show that such transformations can also generate equilibrium configurations where an additional charge of a third specie is present. Relationship with integrable hierarchies is briefly discussed.
Published Version
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