Orateur
Description
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 $\mathbb{C}^+$, connected with each other and/or with the real axis by some 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 $K\subset\mathbb{C}$ of minimal logarithmic capacity that contains a given set of anchors $E\subset\mathbb{C}$. In this talk we discuss the modified Chebotarev’s problem, where $E$ and $K$ are subsets of $\mathbb{C}^+$ and where we minimize the Dirichlet energy of the Green potential (for $\mathbb{C}^+$) in $\mathbb{C}^+ \setminus K$ instead of the logarithmic capacity of $K$. This is a joint work with M. Bertola.