Abstract: Soliton gases for integrable systems is a rapidly developing new area in the theory of nonlinear waves. For a given spectral support set, a soliton gas of maximal average intensity is called soliton condensate. A spectral support set for a fNLS soliton condensate is often represented by a finite collection of points (anchors) E in the upper half plane H, connected with each other and/or with the real axis by some set of (Schwarz symmetrical) arcs. Given a set of anchors E, a natural question is to find a collection of such arcs that produces fNLS soliton condensate of minimal average intensity. That leads to a modification of the well-known Chebotarev’s continuum problem, which consists in finding a continuum K ⊂ C of minimal logarithmic capacity that contains a given set of anchors E ⊂ C. In this talk, we discuss our solution to the modified Chebotarev’s problem, where E and K are subsets of the upper half plane H and where we minimize the Dirichlet energy of H \ K instead of the logarithmic capacity of K. This is a joint work with Marco Bertola.